Question

Jace works two summer jobs. He receives $8/hour at a fast food restaurant and $13/hour mowing lawns. Jace wants to make at least $1500 over the summer. His hours should not exceed 200 for the summer. Which ordered pair, (F, M), is a solution to the system of inequalities?

a) (F = 125, M = 100)
b) (F = 150, M = 50)
c) (F = 100, M = 150)
d) (F = 50, M = 150)

Answer 1

The ordered pair that is a solution to the system of inequalities, given Jace's wage rates and constraints, is (F = 150, M = 50) which satisfies both the minimum income requirement and the maximum hours limit.

Step-by-step explanation:

The student is asking to find an ordered pair (F, M) that represents the hours worked at a fast food restaurant (F) and mowing lawns (M) that would satisfy the constraints of making at least $1500 over the summer and not exceeding 200 hours of work in total.

To solve this, we need to set up inequalities based on the given conditions. The first condition is that Jace wants to make at least $1500: 8F + 13M ≥ 1500. The second condition is that the total hours should not exceed 200: F + M ≤ 200.

Now we need to test each ordered pair to see which one fits these conditions:

• (F = 125, M = 100) does not satisfy the second condition because 125 + 100 > 200.
• (F = 150, M = 50) satisfies both conditions because 8(150) + 13(50) = 1700 ≥ 1500 and 150 + 50 = 200 ≤ 200.
• (F = 100, M = 150) does not satisfy the second condition because 100 + 150 > 200.
• (F = 50, M = 150) satisfies the first condition because 8(50) + 13(150) = 2350 ≥ 1500, but not the second because 50 + 150 > 200.

Thus, the correct answer is b) (F = 150, M = 50).