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 20 child bikes and 6 adult bikes in the week. (2 points) A: No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 B: No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 C: Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 D: Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answer 1

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

Explanation:

I took the test on FLVS

Answer 2

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

Explanation:

c = child bike

a = adult bike

Child bike requirement:

4 hours build time

4 hours test time

Adult bike requirement:

6 hours build time

4 hours test time

Available Building time per week ≤ 120 hours

Available Testing time per week ≤ 100 hours

Therefore, company's work schedule is;

Building:

4c + 6a ≤ 120

Testing:

4c + 4a ≤ 100

Combined:

4c + 6a ≤ 120 and 4c + 4a ≤ 100

Building 20 Child bike and 6 adult bike in a week:

4(20) + 6(6) ≤ 120 and 4(20) + 4(6) ≤ 100

80 + 36 ≤ 120 - - - - 80 + 24 > 100

Therefore Building 20 Child bike and 6 adult bike in a week is not feasible.