Question

Karen earns $8 per hour shoveling snow and $10 per hour babysitting. She wants to earn more than $80 per week but work fewer than 12 hours. The system of inequalities shown represents the number of hours of shoveling, s, and the number of hours of babysitting, b, she must complete to reach her goal.

8s + 10b > 80

s + b < 12

Which are possible solutions for the number of hours Karen can work at each job and still reach her goals? Check all that apply.

2 hours shoveling snow; 6 hours babysitting
2 hours shoveling snow; 8 hours babysitting
4 hours shoveling snow; 7 hours babysitting
6 hours shoveling snow; 6 hours babysitting
8 hours shoveling snow; 3 hours babysitting

Answer 1

This is similar to the last problem; if her goal is to earn $80 and she must work fewer than 12 hours, I would first check to make sure none of the choices have her work more than 12 hours; none of them do. With that covered, since there can be multiple answers, you must check each solution one by one.
1. 2 snow shoveling hrs * 8 dollars + 6 babysitting hours * 10 dollars = 16 + 60 = $76. This answer does not work.
2. 2 snow shoveling hrs * 8 dollars + 8 babysitting hrs * 10 dollars = 16 + 80 = $96.
This answer works.
3. 4 snow shoveling hrs * 8 dollars + 7 babysitting hrs * 10 dollars = 32 + 70 = $102.
This answer works.
4. 6 snow shoveling hrs * 8 dollars + 6 babysitting hrs * 10 dollars = 48 + 40 = $108.
This answer works.
5. 8 snow shoveling hrs * 8 dollars + 3 babysitting hrs * 10 dollars = 64 + 30 = $94.
This answer works.

Therefore, all answers work but the first choice.