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

Although I replied late, nobody gave the answer.

The answer you are looking for is C). But how do you know it's correct? Do some calculation.

Child bike: 4 hours to build + 4 hours to test = 8 hours total

Adult bike: 6 hours to build + 4 hours to test = 10 hours total

5*4 = 20 build hours for child bikes

5*4 = 20 test hours for child bikes

15*6 = 90 build hours for adult bikes

15*4 = 60 test hours for adult bikes

20 + 20 = 40 total hours for child bikes

90 + 60 = 150 total hours for adult bikes

20 + 60 = 80 total test hours

20 + 90 = 110 build hours

Since this amount is below the maximum, the bike order DOES meet the restrictions.

Our equations should be 4c + 6a ≤ 120 for the total building hours, and 4c + 4a ≤ 100 for the total testing hours.

In conclusion, the answer is C) Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.

Answer 2

I'm sorry I have no clue I'm not that smart but I would just like to say that I like your profile picture