Question

Alfonso makes $8.00 per hour working at a movie theater and $12.00 per hour working at a restaurant. Next week, Alfonso is scheduled to work 6 hours at the movie theater. Which of the following inequalities represent the amount of hours (h) that Alfonso needs to work at the restaurant next week to earn at least $144 between his two jobs?

A. 8*6+12h≥144
B. 8h+12*6≥144
C. 8h+12h≥144
D. 8*6+12*6≥144h

Answer 1

Next week, Alfonso will work 6 hours at the theater, where he is payed $8 per each hour he works there. So, he is going to make a total of 6*$8=$48.

Let h be the number of hours that Alfonso needs to work at the restaurant to make a total of at least $144.

Since working at the restaurant he makes $12 per hour, then per h hours, he is going to make 12h dollars.


In total, he is going to make 48 + 12h dollars, and we want this sum to be at least $144, thus, we set the inequality:

48 + 12h≥144.

Answer: A

Answer 2

The answer is:
A) 8*6 + 12*h ≥ 144

The 8*6 is the money he will have after working at the theatre (6 hours, $8/hr)
12*h is the money he'll earn at the restaurant in h hours.

In order to comply with the inequality, the left side must be greater than or equal to the right side. The value of h that satisfies this is the domain of h.