example 6 you have two summer jobs at a youth center. you earn $8 per hour teaching basketball and...

6

Example 6 You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the amount of time (in hours) you teach basketball each week, and let y represent the amount of time (in hours) you teach swimming each week. Your goal is to earn at least $200 per week. JOB EARNINGS • Write an inequality that describes your goal in terms of x and y. • Graph the inequality. • Give three possible combinations of hours that will allow you to meet your goal. Solve a multi-step problem

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Page 1: Example 6 You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the

Example 6

You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the amount of time (in hours) you teach basketball each week, and let y represent the amount of time (in hours) you teach swimming each week. Your goal is to earn at least $200 per week.

JOB EARNINGS

• Write an inequality that describes your goal in terms of x and y.• Graph the inequality.• Give three possible combinations of hours that will allow you to meet your goal.

Solve a multi-step problem

Page 2: Example 6 You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the

Solve a multi-step problemExample 6

STEP 2 Graph the inequalityFirst, graph the equationin Quadrant I. The inequality is ≥ , so usea solid line.

200.10y8x + ≥

20010y8x + =

Next, test in :( )5, 5 20010y8x + ≥

SOLUTION

STEP 1 Write a verbal model. Then write an inequality.

•8 x + 10 • y ≥ 200

Page 3: Example 6 You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the

Solve a multi-step problemExample 6

200+( )58 ( )510?≥

Finally, shade the part of Quadrant I that does not contain , because is not a solution of the inequality.

( )5, 5 ( )5, 5

20090 ≥

Page 4: Example 6 You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the

Solve a multi-step problemExample 6

Basketball time (hours) 13 14 16

12 10 9

224 212 218

Swimming time (hours)

Total earnings (dollars)

STEP 3 Choose three points on the graph, such as , , and . The table shows the total earnings for each combination of hours.

( )13, 12 ( )14, 10 ( )16, 9

Page 5: Example 6 You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the

Guided Practice

8. WHAT IF?

for Example 6

In Example 6, suppose that next summer you earn $9 per hour teaching basketball and $12.50 per hour teaching swimming. Write and graph an inequality that describes your goal. Then give three possiblecombinations of hours that will help you meet your goal.

Page 6: Example 6 You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the

Guided Practice for Example 6

ANSWER 9x + 200, 12.5y ≥

( ),8, 12 ( ),12, 10 ( )16, 6Sample answer:

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