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.
1) No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
2) No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
3) Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
4) Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answer 1

Answer:

4c + 6a < = 120 ...4(20) + 6(6) = 116 <== correct

4c + 4a < = 100....4(20) + 4(6) = 104 <== incorrect

"first answer"choice

HOPE IT HELPS!!!

Answer 2

Concept:

Inequality is a relation that defines a non-equal comparison between the given two numbers or other mathematical expressions.

Given:

One child bike requires 4 hours to build and 4 hours to test. Similarly, one adult bike requires 6 hours to build and 4 hours to test. From the number of workers in the company, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week.

Find:

If c represents child bikes and a represents adult bikes, the system of inequality which can say that the company can build 10 child bikes and 12 adult bikes in the week.

Solution:

Let the no. of child bikes is c and the no. of adult bikes be a.

For the building of bikes,

4c + 6a ≤ 120

For the testing of bikes,

4c + 4a ≤ 100

Checking the equations, for given 10 child bikes and 12 adult bikes in the week.

For the building of bikes,

( 4 × 10 ) + ( 6 × 12 ) ≤ 120

40 + 72 ≤ 120

112 ≤ 120 (Inequality satisfied)

For the testing of bikes,

( 4 × 10 ) + ( 4 × 12 ) ≤ 100

40 + 48 ≤ 100

88 ≤ 100 (Inequality satisfied)

Hence, the correct option is (c) Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.

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