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

Yes, because the bike order meets the restrictions of
`4c+6a\leq 120` and
`4c+4a\leq 100`

Explanation:

Let c represents the child bike

Let a represents the adult bike

Now Each child bike requires 4 hours to build

So, c child bike requires time to build = 4c

Each adult bike requires 6 hours to build

So, a adult bike requires time to build = 6a

We are also given that the company is able to have up to 120 hours of building time

So, the equation becomes:

`4c+6a\leq 120` --1

Each child bike requires 4 hours to test

So, c child bike requires time to test = 4c

Each adult bike requires 4 hours to test

So, a adult bike requires time to test = 4a

We are also given that the company is able to have up to 100 hours of testing time for a week.

So, the equation becomes:

`4c+4a\leq 100` --2

With 1 and 2

The system of equations represent the situation :

`4c+6a\leq 120`

`4c+4a\leq 100`

Now we are given that whether the company can build 10 child bikes and 12 adult bikes in the week.

So, substitute c =10 and a = 12 in both equations.

Equation 1:
`4c+6a\leq 120`

`4(10)+6(12)\leq 120`

`40+72\leq 120`

`112\leq 120`

Equation 2:
`4c+4a\leq 100`

`4(10)+4(12)\leq 100`

`40+48\leq 100`

`88\leq 100`

Thus the bike order meets the restrictions of
`4c+6a\leq 120` and
`4c+4a\leq 100`

Thus Option C is correct : Yes, because the bike order meets the restrictions of
`4c+6a\leq 120` and
`4c+4a\leq 100`

Answer 2

So every youngster bicycle takes 8 hours to make - 4 assemble, 4 test.
Furthermore, every grown-up bicycle takes 10 hours to make - 6 fabricate, 4 test.
10 Tyke bicycles is 40 hours of assembling and 40 hours of testing.
12 grown-up bicycles is 72 hours of assembling and 48 hours of testing
72+40 = 112 (out of 120 hours)
40+48 = 88 (out of 100 hours).
So they can meet said quantity.
The right answer would be the second last choice which is Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.