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.

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

Option A is correct.

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

Explanation:

here, c represents child bikes and a represents the adult bikes.

As per the statement:

Each child bike requires 4 hours to test, each adult bike 4 hours to test and the company is able to have up to 100 hours of testing time.

then the inequality based on the hour available to test is:

`4c+4a\leq 100` .....[1]

It is also given that:

Each child bike requires 4 hours to build, each adult bike 6 hours to build and the company is able to have up to 120 hours of building time.

then the inequality based on the hour available to building is:

`4c+6a\leq 120` ......[2]

then the system of inequalities given as:

`4c+4a\leq 100`

`4c+6a\leq 120`

we have to tell whether the company can build 20 child bikes and 6 adult bikes in the week.

Substitute the value of :

c = 20 and a = 6 in the system of inequalities:

`4(20)+4(6) = 80+24 = 104\leq 100` false

`4(20)+6(6)= 80+36 = 116 \leq 120` True

Therefore, the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.