HELP PLEASE
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

[tex]4c+6a \leq 120[/tex] (As each child bike takes 4 hours to build and each adult bike takes 6 hours to build, and the company has building time up to 120 hours)

[tex]4c +4a\leq 100[/tex] (As each child bike takes 4 hours to test and each adult bike takes 4 hours to test, and the company has testing time up to 100 hours)

We will substitute 20 for 'c' and 6 for 'a'

[tex]4(20)+6(6) \leq 120[/tex]

[tex]80+36 \leq 120[/tex]

[tex]116 \leq 120[/tex]

This is true.

For the second inequality;

[tex]4(20)+4(6) \leq 100[/tex]

[tex]80+24 \leq 100[/tex]

[tex]104 \leq 100[/tex]

So, this is not true.

Hence, option 1st is true.