Question

lynnsey plans to earn at least $300 babysitting and mowing lawns this summer. she will charge $12 per hour for babysitting, and $15 per hour for mowing lawns. she would like to work a maximum of 50 hours this summer.she wrote the following system of inequalities to determine combinations of jobs she can do. let $x$ = number of hours spent babysitting, and $y$ = number of hours spent mowing lawns.$\begin{cases}12x + 15y geq 300 \\x + y leq 50end{cases}$select each choice that will earn her at least $300, but will not require more than 50 hours of work.a 15 hours of babysitting and 20 hours of mowing lawns.b 15 hours of babysitting and 5 hours of mowing lawns.c 10 hours of babysitting and 10 hours of mowing lawns.d 0 hours of babysitting and 15 hours of mowing lawns.e 10 hours of babysitting and 15 hours of mowing lawns.f 40 hours of babysitting and 5 hours of mowing lawns.

Explanation:

Step1: Define check conditions

We need to verify two conditions for each option:

1. Total earnings: $12x + 15y \geq 300$
2. Total hours: $x + y \leq 50$

where $x$ = babysitting hours, $y$ = mowing hours.

Step2: Check Option A

$x=15, y=20$
Total hours: $15+20=35 \leq 50$
Earnings: $12(15)+15(20)=180+300=480 \geq 300$
Both conditions satisfied.

Step3: Check Option B

$x=15, y=5$
Total hours: $15+5=20 \leq 50$
Earnings: $12(15)+15(5)=180+75=255 < 300$
Fails earnings condition.

Step4: Check Option C

$x=10, y=40$
Total hours: $10+40=50 \leq 50$
Earnings: $12(10)+15(40)=120+600=720 \geq 300$
Both conditions satisfied.

Step5: Check Option D

$x=0, y=15$
Total hours: $0+15=15 \leq 50$
Earnings: $12(0)+15(15)=0+225=225 < 300$
Fails earnings condition.

Step6: Check Option E

$x=10, y=15$
Total hours: $10+15=25 \leq 50$
Earnings: $12(10)+15(15)=120+225=345 \geq 300$
Both conditions satisfied.

Step7: Check Option F

$x=40, y=5$
Total hours: $40+5=45 \leq 50$
Earnings: $12(40)+15(5)=480+75=555 \geq 300$
Both conditions satisfied.

Answer:

A. 15 hours of babysitting and 20 hours of mowing lawns
C. 10 hours of babysitting and 40 hours of mowing lawns
E. 10 hours of babysitting and 15 hours of mowing lawns
F. 40 hours of babysitting and 5 hours of mowing lawns