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) Group of answer choices 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

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

Explanation:

It is given that, each child bike requires 4 hours to build and each adult bike requires 6 hours to build.

Hence, c child bikes and a adult bikes require
`(4c + 6a)` hours to build.

It is also given that, each child bike requires 4 hours to test and each adult bike requires 4 hours to test.

Total time to test, c child bikes and a adult bikes is
`(4c + 4a)`

The company will be able to make c child bikes and a adult bikes if
`(4c + 6a) \leq 120\\(4c + 4a)\leq 100`

If c = 20 and a = 6, then (4c + 6a) = 116 < 120.

and (4c + 4a) = 104 > 100.