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.

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 ≤
d. 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 4c + 6a ≤ 120 and 4c + 4a ≤ 100.

Explanation:

According to the described situation, the system of inequalities that best explains whether the company can build 20 child bikes and 6 adult bikes in the week is given by:

What is the system of inequalities?

Considering the variables c and a, for the number of child and adult bikes, respectively, we have that, considering the building time:

testing time When c = 20, a = 6:

Hence, the correct option is:

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