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. 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

First we have to find the constraints. 
$4c+6a$ is the total amount of time spent to build the child and the adult bike. Since this time cannot exceed 120, then we get the inequality:
$4c+6a< 120$
We do the same work for testing time and get the constraint:
$4c+4a< 100$
Now let check the case c=10 and a=12:
4*10+6*12=112 and this number is less than 120, Ok. 
Second contraint:
 4*10+4*12=88, the number again is less than 100, OK. 

Our answer is than YES, the correct answer is the third one.