EXAMPLE 4 Solve a multi-step problem

As a scuba diver descends into deeper water, the pressure of the water on the diver’s body steadily increases.

SCUBA DIVING

The pressure at the surface of the water is 2117 pounds per square foot (lb/ft2). The pressure increases at a rate of 64 pounds per square foot for each foot the diver descends. Find the depth at which a diver experiences a pressure of 8517 pounds per square foot.

SOLUTION

EXAMPLE 1

Write a verbal model. Then write an equation.

Find the depth at which the pressure is 8517 pounds per square foot.

P = 2117 + 64d Write equation.

STEP 1

STEP 2

EXAMPLE 4 Solve a multi-step problem

GUIDED PRACTICE

Substitute 8517 for P.

8517 – 2117 = 2117 – 2117 + 64d Subtract 2117 from each side.

8517 = 2117 + 64d

6400 = 64d Simplify.

Divide each side by 64.

100 = d Simplify.

ANSWER

A diver experiences a pressure of 8517 pounds per square foot at a depth of 100 feet.

64640064 = 64d

EXAMPLE 4 Solve a multi-step problem

GUIDED PRACTICE

P = 2117 + 64d Write original equation.

Substitute 8517 for P and 100 for d.

Multiply 64 and 100.

Simplify. Solution checks.

8517 2117 + 6400?=

8517 2117 + 64(100)?=

CHECK

EXAMPLE 4 Solve a multi-step problem

8517 = 8517

GUIDED PRACTICE for Example 4

WHAT IF? In Example 4, suppose the diver experiences a pressure of 5317 pounds per square foot. Find the diver’s depth.

9

SOLUTION

Find the depth at which the pressure is 5314 pounds per square foot.

STEP 1

P = 2117 + 64d Write equation.

Substitute 5317 for P.

5317 – 2117 = 2117 – 2117 + 64d

5317 = 2117 + 64d

3200 = 64d Simplify.

Subtract 2117 from each side.

GUIDED PRACTICE for Example 4

Divide each side by 64.

50 = d Simplify.

64320064 = 64d

ANSWER

A diver experiences a pressure of 5317 pounds per square foot at a depth of 50 feet.

GUIDED PRACTICE for Example 4

10. Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work?

Jobs

Substitute 53 for P.

53–13 = 13 –13 + 8h

53 = 13 + 8h

40 = 8h Simplify.

Subtract 13 from each side.

SOLUTION

P = 13 + 8h Write equation.

5 = h Simplify.

GUIDED PRACTICE for Example 4

ANSWER

She worked for 5 hours