Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per week. This week, her goal is to make at least $75.

A. Use a system of inequalities to model the scenario above. Let x represent babysitting hours and y represent tutoring hours.

B. Use the model created in part A to create a graph representing Jeanne's probable income earned and possible number of hours worked this week.

C. Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model.

Question

Mathematics

Guest

7 April, 16:38

Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per week. This week, her goal is to make at least $75.

A. Use a system of inequalities to model the scenario above. Let x represent babysitting hours and y represent tutoring hours.

B. Use the model created in part A to create a graph representing Jeanne's probable income earned and possible number of hours worked this week.

C. Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model.

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Answers (1)

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Ralph Lewis · Answer 1

A.

If we l et x represent babysitting hours and y represent tutoring hours:

x + y ≤ 20

6x + 10y ≥ 75

B. The inequality: x + y ≤ 20 can be graphed by graphing the line x + y = 20 and shading the area below the line.

The inequality 6x + 10y ≥ 75 can be graphed by graphing the line 6x + 10y = 75 and shading the area above the line.

C. The area where the two shaded regions from the two inequalities overlap are the possible number of hours for tutoring and for babysitting. Algebraically:

x ≤ 20 - y

6 (20 - y) + 10y ≥ 75

y ≤ 11.25

x ≤ 8.75