6th Grade Math Textbook, Fundamentals

Lesson 6-4 for exercise sets. Chapter 6 155

Practice & Activities

Write and solve a proportion to solve the problem.

1.A sample of paint contains 3 ounces of blue paint and 8 ounces of yellow

paint. If you have a 24-ounce can of the blue paint, how much yellow paint

should you mix with it in order to make the same color as the sample?

2.Discuss and Write Explain how a rate of 20 pages an hour would affect

the graph in the example above.

A mass hanging on a spring causes the spring to stretch. The length of the

spring when stretched is in direct proportion to the force applied by the

mass. If a 3-kilogram mass stretches a spring so that it is 63 centimeters long,

what will be the length of the spring if the force of a 5-kilogram mass is used?

Let xthe length of the spring if a 5-kg mass is used.

Method 1 Use Like Units



Solve: 

63 • 5  3 x

315  3 x



x 105

Check: Substitute 105 for x.

63 • 5 105 • 3 Cross multiply.

315  315 Tr u e

The spring will be 105 cm long if a 5-kg mass is used.

?



3

5

?

10563 

Divide both sides

by 3 to isolate x.

3 x

3

315

3

Use the Cross-

Products Rule.

3

5

63

x

3 kg

5 kg

63 cm

x

mass

mass

length

length

Method 2 Use Unlike Units



Solve: 

5(63)  3 x

315  3 x



x 105

Check: Substitute 105 for x.

63(5) (105)3 Cross multiply.

315  315 Tr u e

length

mass

?



105

5

?

(^633) 
Divide both sides
by 3 to isolate x.
3 x
3
315
3
Use the Cross-
Products Rule.
x
5
63
3
x
5 kg
63 cm
3 kg
length
mass
1

You can represent a direct proportion as a graph.

Write the equivalent ratios. Then plot the coordinates.

25 pages read in 1 hour 25 : 1 (1, 25)

50 pages read in 2 hours 50 : 2 (2, 50)

75 pages read in 3 hours 75 : 3 (3, 75)

The ratios form a direct proportion:  .

The graph is a straight line slanting upward from left to right.

The number of pages Mike reads and the number of hours are in direct proportion.

75

3

50

2

25

1











Number of Pages

Time (h)

   

Mike’s Reading Rate