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

Answer 1

Answer:

$4c+6a\leq120\\\\4c+4a\leq100$

Step-by-step explanation:

Let c represents child bikes and a represents adult bikes.

Given :  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.

Then, the required system of inequality :-

$4c+6a\leq120----(1)\\\\4c+4a\leq100-----(2)$

If company make 10 child bikes and 12 adult bikes in the week.

Then Put c=10 and a=12 bikes in (1) and (2).

$4(10)+6(12)=40+72=112\leq120$⇒Bike order meets the restrictions

$4(10)+4(12)=40+48=88\leq100$⇒Bike order meets the restrictions

Hence, the system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week.

$4c+6a\leq120\\\\4c+4a\leq100$