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Setting up proportions to solve word problems | 7th grade | Khan Academy

Video vocabulary

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

set

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US / set /

UK / sɛt /

A1
  • adjecitve
  • Prepared for something; ready
  • noun
  • Complete group of something
  • Place where a television show or movie is filmed
  • Group of games in a tennis match
  • Device that receives radio or television signals
  • verb
  • To make a clock state or ring at a particular time
  • To decide upon or choose something
  • To make something ready for use (e.g. table)
  • To decide on a price for something
  • To become hard (of glue, concrete etc.)
  • To be located in a specific place or time
  • To put (e.g. a vase) down carefully in a place
  • To put someone in a certain condition or state
  • (Of the sun) to go lower than the horizon

magenta

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US / məˈdʒentə /

UK / məˈdʒɛntə /

C1
  • noun
  • Deep purplish red

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

constant

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US / 'kɒnstənt /

UK / ˈkɑnstənt /

A2
  • adjecitve
  • Happening frequently or without pause
  • noun
  • Thing that happens always or at a regular rate

cake

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US / keɪk /

UK / keɪk /

A1
  • noun
  • Sweet baked food made from flour, eggs, fat, sugar
  • verb
  • To cover with a thing that becomes hard when dried
  • To become dried into a hardened mass

situation

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US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

green

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US / gri:n /

UK / ɡrin /

A1
  • adjecitve
  • Color of young leaves
  • Covered with vegetation, e.g. grass
  • Concerned about protecting the environment
  • The color of young leaves
  • Lacking in experience/knowledge due to being young
  • Being not fully grown or ripe, as in fruit
  • noun
  • Large grassy area
  • used as a part of a name of a place (UK)

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

last

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US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

problem

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US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

notice

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US / 'nəʊtɪs /

UK / ˈnotɪs /

A1
  • noun
  • Time by when you must leave, e.g. if you are fired
  • Paper with an announcement, e.g. pinned to a board
  • verb
  • To become aware by sight, touch, or hearing

ratio

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US / ˈreɪʃiəʊ /

UK / ˈreɪʃioʊ /

C2
  • noun
  • The relationship in relative size, etc.

new

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US / nju: /

UK / nu, nju /

A1
  • adjecitve
  • Not old, recently born, built or made
  • Being or doing something for the first time
  • Not felt, seen or known previously
  • Having been recently bought or obtained

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

either

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US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • adjecitve
  • One of two (used when there is a choice of two)
  • adverb
  • (After negative statements) likewise, in addition
  • conjunction
  • Used as the first of two connected things
  • determiner
  • Used as the first of two connected things
  • pronoun
  • The one or the other

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

should

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US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

marker

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US / ˈmɑ:kə(r) /

UK / ˈmɑ:rkə(r) /

B1
  • noun
  • Something that is easy to recognize or identify
  • Thick pen used for writing, e.g. on boards

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

scenario

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US / sɪˈnɑː.ri.əʊ /

UK / səˈner.i.oʊ /

B1
  • noun
  • An imagined sequence of events in a plan/project

many

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US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

describe

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US / dɪ'skraɪb /

UK / dɪˈskraɪb /

A1
  • verb
  • To tell the appearance, sound, smell of something

always

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US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

once

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US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

obviously

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US / ˈɒbviəsli /

UK / ˈɑːbviəsli /

A2
  • adverb
  • In a way that is obvious/easy to see or understand

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

mathematic

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US / ˌmæθɪ'mætɪk /

UK / ˌmæθə'mætɪk /

A1
  • other

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

anything

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US / ˈeniθɪŋ /

UK / ˈɛniˌθɪŋ /

A1
  • pronoun
  • A thing of any kind

recipe

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US / 'resəpɪ /

UK / ˈrɛsəˌpi /

B1
  • noun
  • Conditions likely to create a particular result
  • Directions for making a dish, with the ingredients

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

call

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US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

proportion

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US / prəˈpɔ:ʃn /

UK / prəˈpɔrʃən, -ˈpor- /

A2
  • noun
  • A part of a whole thing
  • State of balance between two or more things
  • Size of one thing compared to the size of another
  • verb
  • To balance the size of something with another

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

completely

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US / kəmˈpli:tli /

UK / kəmˈpliːtli /

A1
  • adverb
  • In every way or as much as possible

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

egg

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US / eg /

UK / ɛɡ /

A2
  • noun
  • Hard-shelled thing from which a young bird is born

require

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US / rɪ'kwaɪə(r) /

UK / rɪˈkwaɪr /

A2
  • verb
  • To demand that someone does something
  • To need to do something, to make it necessary

case

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US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

apple

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US / ˈæpl /

UK / ˈæpəl /

A1
  • noun
  • Hard round red or green fruit with a white center

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

people

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US / 'pi:pl /

UK / ˈpipəl /

A1
  • noun
  • Persons sharing culture, country, background, etc.
  • Men, Women, Children

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

essentially

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US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

solve

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US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

example

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US / ɪgˈzɑ:mpl /

UK / ɪɡˈzæmpəl /

A1
  • noun
  • Thing, person which represents a category

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

between

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US / bɪˈtwi:n /

UK / bɪˈtwin /

A1
  • preposition
  • From one person, thing, or place, to another
  • In the space that separates two objects
  • Among two or more people who share something

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

figure

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US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

valid

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US / 'vælɪd /

UK / ˈvælɪd /

A2
  • adjecitve
  • Being in effect or in force, often legally
  • Reasonable; based on sound assumptions
  • Working correctly; producing results

word

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US / wɜ:d /

UK / wɚd /

A1
  • noun
  • Unit of language that has a meaning
  • Promise
  • Short remark or piece of information
  • verb
  • To express something by choosing particular words

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

flip

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US / flɪp /

UK / flɪp /

B2
  • noun
  • Act of turning your body in the air; somersault
  • Movement of something from one position to another
  • verb
  • To turn your body in the air, as in gymnastics
  • To move into a different position quickly
  • To move a button or switch to turn on or off

three

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US / θri: /

UK / θri /

A1
  • number
  • Number 3

answer

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US / 'ɑ:nsə(r) /

UK / ˈænsɚ /

A1
  • noun
  • Reply to a question someone asks
  • Solution to a problem or test question
  • verb
  • To reply to a question someone asks
  • To solve a test question or a problem

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

kind

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US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

color

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US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

blue

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US / blu: /

UK / blu /

A1
  • adjecitve
  • Color of the clear sky
  • Feeling sad or down

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

represent

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US / ˌreprɪ'zent /

UK / ˌrɛprɪˈzɛnt /

A2
  • verb
  • To depict art objects, figures, scenes; to portray
  • To show or describe something in a particular way
  • To act on behalf of others in government
  • To act or speak for another person or other people

good

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US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite
  • Subtitles section
  • I have three word problems here.
  • And what I want to do in this video is not solve the word problems but just set up the equation that we could solve to get the answer to the word problems.
  • And essentially, we're going to be setting up proportions in either case.
  • So in this first problem, we have 9 markers cost $11.50.
  • And then they ask us, how much would 7 markers cost?
  • And let's just set x to be equal to our answer.
  • So x is equal to the cost of 7 markers.
  • So the way to solve a problem like this is to set up two ratios and then set them equal to each other.
  • So you could say that the ratio of 9 markers to the cost of 9 markers, so the ratio of the number of markers, so 9, to the cost of the 9 markers, to 11.50, this should be equal to the ratio of our new number of markers, 7, to whatever the cost of the 7 markers are,
  • to x.
  • Let me do x in green.
  • So this is a completely valid proportion here.
  • The ratio of 9 markers to the cost of 9 markers is equal to 7 markers to the cost of 7 markers.
  • And then you could solve this to figure out how much those 7 markers would cost.
  • And you could flip both sides of this, and it would still be a completely valid ratio.
  • You could have 11.50 to 9.
  • The ratio between the cost of the markers to the number of markers you're buying, 11.50 to 9, is equal to the ratio of the cost of 7 markers to the number of markers, which is obviously 7.
  • So all I would do is flip both sides of this equation right here to get this one over here.
  • You could also think about the ratios in other ways.
  • You could say that the ratio of 9 markers to 7 markers is going to be the same as the ratio of their costs, is going to be equal to the ratio of the cost of 9 markers to the cost of 7 markers.
  • And then, obviously, you could flip both of these sides.
  • Let me do that in the same magenta color.
  • The ratio of 7 markers to 9 markers is the same thing as the ratio of the cost of 7 markers to the cost of 9 markers.
  • So that is 11.50.
  • So all of these would be valid proportions, valid equations that describe what's going on here.
  • And then you would just have to essentially solve for x.
  • So let's do this one right over here.
  • 7 apples cost $5.
  • How many apples can I buy it with $8?
  • So one again, we're going to assume that what they're asking is how many apples-- let's call that x.
  • x is what we want to solve for.
  • So 7 apples costs $5.
  • So we have the ratio between the number of apples, 7, and the cost of the apples, 5, is going to be equal to the ratio between another number of apples, which is now x, and the cost of that other number of apples.
  • And it's going to be $8.
  • And so notice here in this first situation, what was unknown was the cost.
  • So we kind of had the number of apples to cost, the number of apples to cost.
  • Now in this example, the unknown is the number of apples, so number of apples to cost, number of apples to cost.
  • And we could do all of the different scenarios like this.
  • You could also say the ratio between 7 apples and x apples is going to be the same as the ratio between the cost of 7 apples and the cost of 8 apples.
  • Obviously, you can flip both sides of these in either of these equations to get two more equations.
  • And any of these would be valid equations.
  • Now let's do this last one.
  • I'll use new colors here.
  • A cake recipe for 5 people requires 2 eggs.
  • So we want to know how many eggs-- so this we'll call x.
  • And you don't always have to call it x.
  • You could call it e for eggs.
  • Well, e isn't a good idea, because e represents another number once you get to higher mathematics.
  • But you could call them y or z or any variable-- a, b, or c, anything.
  • How many eggs do we need for a 15-person cake?
  • So you could say the ratio of people to eggs is constant.
  • So if we have 5 people for 2 eggs, then for 15 people, we are going to need x eggs.
  • This ratio is going to be constant.
  • 5/2 is equal to 15/x.
  • Or you could flip both sides of this.
  • Or you could say the ratio between 5 and 15 is going to be equal to the ratio between the number of eggs for 5 people-- let me do that in that blue color-- and the number of eggs for 15 people.
  • And obviously, you could flip both sides of this equation.
  • So all of these, we've essentially set up the proportions that describe each of these problems.
  • And then you can go later and solve for x to actually get the answer.