Abicycle 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.

Step-by-step explanation:

Let 'c' be the number of child bikes  c=20

and 'a' be the number of adult bikes. a=6

According to the problem  

The restriction of building time for a week is 4c+6a≤120 hours(1)

and the restriction of testing time for a week is 4c+4a≤100 hours(2)

Lets check whether company can build c=20 and a=6 bikes in a week by putting these values in (1) and (2).

4c+6a≤120 hours(1)

4(20)+6(6)≤120

80+36≤120

116≤120 (true)

4c+4a≤100 hours(2)

4(20)+4(6)≤100

80+24≤100

104≤100 (true)

Hence,  the company can build 20 child bikes and 6 adult bikes in the week