Question

Oct 29, 10:22:04 PM

Juan is working two summer jobs, making $12 per hour babysitting and making $16

per hour lifeguarding. In a given week, he can work at most 17 total hours and must

earn at least $240. If Juan worked 3 hours babysitting, determine all possible values

for the number of whole hours lifeguarding that he must work to meet his

requirements.

Answer 1

He must need to work 13 hours or 14 hours for lifeguarding.

Explanation:

Consider the provided information.

Let x represents the number of hours for babysitting.

y represents the number of hours for life-guarding.

In a given week, he can work at most 17 total hours and must

`x+y\leq 17`

Juan is working two summer jobs, making $12 per hour babysitting and making $16 per hour lifeguarding. He must earn at least $240.

`12x+16y\geq 240`

If Juan worked 3 hours babysitting,

Substitute x=3 in
`x+y\leq 17`

`3+y\leq 17`

`y\leq 14`

Thus, he can work at most 14 hours for lifegurading.

Substitute x=3 in
`12x+16y\geq 240`

`12(3)+16y\geq 240`

`36+16y\geq 240`

`16y\geq 204`

`y\geq 12.75`

Therefore, he must need to work 13 hours or 14 hours for lifeguarding.