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

This is the 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

Now you can state the system of inequalities from the statements

1) First inequality based on the hours availble to buiding

Each child bike requires 4 hours, e ach adult bike requires 6 hours to build and the company is able to have up to 120 hours of building = >

4c + 6a ≤ 120

2) Second inequality based of the hours available to testing.

Each child bike requires 4 hours to test, each adult bike 4 hours to test and the company is able to have up 100 hours of testing time for a week = >

4c + 4a ≤ 100

Then the two inequalities are:

4c + 6a ≤ 120

4c + 4a ≤ 100

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

Which you can verify by replacing in both equations 10 for c and 12 for a. Look:

1) 4 (10) + 6 (12) = 40 + 72 = 112 ≤ 120

2) 4 (10) + 4 (12) = 40 + 48 = 88 ≤ 100