Question

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week.
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answer 1

C testing hours: 4c
a testing hours: 4a
Total testing hours available = 100
100 ≥ 4c + 4a
c building hours: 4c
a building hours: 6a
Total building hours available = 120
120 ≥ 4c + 6a 
Substituting the values of c, 10, and a, 12, to see if both inequalities are satisfied:
building:
120 ≥ 4(10) + 6(12) = 120 ≥ 112; satisfied
testing:
100 ≥ 4(10) + 4(12) = 100 ≥ 88; satisfied
So yes, the bike order can be met because the restrictions we created are met. The third option is correct.