Question

ruby is working two summer jobs, making $12 per hour washing cars and making $8 per hour walking dogs. in a given week, she can work at most 18 total hours and must earn a minimum of $180. if ruby worked 3 hours walking dogs, determine all possible values for the number of whole hours washing cars that she must work to meet her requirements.

Explanation:

Step1: Define variable for car washing hours

Let $x$ = whole hours washing cars.

Step2: Calculate dog walking earnings

Earnings from dogs: $3 \times 8 = 24$ dollars

Step3: Set up minimum earnings inequality

Total earnings ≥ $180$:
$12x + 24 \geq 180$

Step4: Solve earnings inequality

Subtract 24 from both sides:
$12x \geq 180 - 24$
$12x \geq 156$
Divide by 12:
$x \geq 13$

Step5: Set up total hours inequality

Total hours ≤ 18:
$x + 3 \leq 18$

Step6: Solve hours inequality

Subtract 3 from both sides:
$x \leq 15$

Step7: Combine constraints (whole hours)

$13 \leq x \leq 15$, $x$ is integer.

Answer:

13, 14, 15 hours