7th Grade Math

278 Proportions and Similarity

You can also use the unit rate to write an equation expressing the

relationship between two proportional quantities.

Write and Use an Equation

GASOLINE Jaycee bought 8 gallons of gasoline for $31.12. Write an

equation relating the cost to the number of gallons of gasoline.

How much would Jaycee pay for 11 gallons at this same rate?

Find the unit rate between cost and gallons.

__cost in dollars

gasoline in gallons^ =

_31.12

8 or $3.89 per gallon

Words

Variable

Equation

The cost is $3.89 times the number of gallons.

Let c represent the cost.

Let g represent the number of gallons.

c = 3.89 · g

Find the cost for 11 gallons sold at the same rate.

c = 3.89g Write the equation.

c = 3.89(11) Replace g with the number of gallons.

c = 42.79 Multiply.

The cost for 11 gallons is $42.79.

e. TYPING Olivia typed 2 pages in 15 minutes. Write an equation

relating the number of minutes m to the number of pages p

typed. If she continues typing at this rate, how many minutes

will it take her to type 10 pages? to type 25 pages?

Solve each proportion.

11 1.5 6 = ^10 p 2. 3.2 9 = 36 n 3. ^41 x = ^52

For Exercises 4 and 5, assume all situations are proportional.

Example 2 4. PAINT Sheila mixed 3 ounces of blue paint with 2 ounces of yellow paint.

She decided to create 20 ounces of the same mixture. Write and solve a

proportion to determine the number of ounces of yellow paint Sheila

needed for the new mixture.

Example 3 5. TUTORING Trina earns $28.50 tutoring for 3 hours. Write an equation

relating her earnings m to the number of hours h she tutors. How much

would Trina earn tutoring for 2 hours? for 4.5 hours?

Example 1

Checking Your Equation Checking Your Equation

You can check to see if

the equation you wrote is

accurate by testing the two

known quantities.

c = 3.89g

31.12 = 3.89(8)

31.12 = 31.12

265_281_C05_L1_895130.indd 278 12/29/09 12:59 PM