Question

christopher is working two summer jobs, making $7 per hour babysitting and making $10 per hour washing cars. in a given week, he can work no more than 16 total hours and must earn a minimum of $130. if x represents the number of hours babysitting and y represents the number of hours washing cars, write and solve a system of inequalities graphically and determine one possible solution.
inequality 1: y geq
inequality 2: y geq
christopher could work
hours babysitting and
hours washing cars.

Explanation:

Step1: Define Variables and Income Inequality

Let \( x \) = hours babysitting, \( y \) = hours washing cars. Income: \( 7x + 10y \geq 130 \). Total hours: \( x + y \leq 16 \). Also, \( x \geq 0 \), \( y \geq 0 \).

Step2: Solve the System

Let's assume \( x + y = 16 \) (max hours). Substitute \( x = 16 - y \) into income inequality:
\( 7(16 - y) + 10y \geq 130 \)
\( 112 - 7y + 10y \geq 130 \)
\( 3y \geq 18 \)
\( y \geq 6 \). Let \( y = 6 \), then \( x = 16 - 6 = 10 \). Check income: \( 7(10) + 10(6) = 70 + 60 = 130 \), which meets the minimum.

Answer:

10 hours babysitting and 6 hours washing cars (or other valid solutions like \( x = 5, y = 10 \) since \( 7(5)+10(10)=35 + 100 = 135 \geq 130 \) and \( 5 + 10 = 15 \leq 16 \), but 10 and 6 is a clear one).