IXL | Compare proportional relationships represented in different ways

Elizabeth and Jayla work at Valley Street Bakery. Today, they are decorating sugar cookies. There is a proportional relationship between the amount of time each person works and the number of cookies she decorates. This table shows how many cookies Elizabeth decorates over time:

Elizabeth's decorating
Time (hours)	Cookies
0.25	7
0.5	14
0.75	21

This equation describes the number of cookies,

that Jayla can decorate in

hours:

Which person decorates cookies at a faster rate?

Elizabeth

Jayla

How many cookies can that person decorate in 2.5 hours?

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Learn with an example

question

Lisa signed up for an art class, and she needs to buy painting supplies. She can buy 3 tubes of oil paint for $19.47. This graph shows the cost of acrylic paint:

Which type of paint costs less per tube?

oil

acrylic

How much less does a tube of that paint cost?

less

key idea

Two quantities have a proportional relationship if they have a constant unit rate. To find the unit rate, divide one quantity by the other quantity.

solution

Find the cost of each type of paint as a unit rate. Then, compare the two rates.

Start with the oil paint. Lisa can buy 3 tubes of oil paint for $19.47. Find the unit rate.

19.47

tubes

6.49

tube

So, oil paint costs $6.49 per

tube.

Next, find the cost per tube of acrylic paint. You can use any point on the line. For example, the point

(

)

tells you that Lisa can buy 5 tubes of oil paint for $25.

Find the unit rate.

tubes

tube

So, acrylic paint costs $5 per

tube.

Now, compare the two unit rates. Since $5 per tube is less than $6.49 per tube, the acrylic paint costs less per tube.

Last, find how much less the acrylic paint costs per tube. Subtract the unit rates.

6.49

per tube

–

per tube

1.49

per tube

So, acrylic paint costs $1.49 less per tube.

Looking for more? Try this:

$Confetti$

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Now entering the Challenge Zone—are you ready?

Teacher tools

Work it out

Not feeling ready yet? These can help:

N.1Find the constant of proportionality from a table

L.9Compare rates: word problems

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