Question

A painter has at most 40 hours to commit to painting a fence and a house next week, with f being the number of hours for the fence and h being the number of hours for the house. For the fence he will charge $20 per hour, and for the house he will charge $25 per hour. He needs to make at least $850 next week. Which four inequalities describe the constraints on the painter next week?
A) f ≥ 0, h ≥ 0, f + h ≤ 40, and 20f + 25h ≥ 850
B) f ≥ 0, h ≥ 0, f + h ≤ 40, and 25f + 20h ≥ 850
C) f ≥ 0, h ≥ 0, f + h ≥ 40, and 20f + 25h ≤ 850
D) f ≥ 0, h ≥ 0, f + h ≥ 40, and 25f + 20h ≤ 850

Answer 1

A) is the answer.

f is greater than 0 because he charges $20/hr.

h is greater than 0 because he charges $25/hr.

f+h added together is less than 40 because he has less than 40 available hours.

20f+25h is greater than $850 because he needs more than $850 next week.