Question

A knitting machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers yesterday. The machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans.

What length of yarn does the machine use to make cardigans and pullovers?

The machine uses ______meters of yarn per cardigan and uses ______

meters per pullover.

Answer 1

1575 meters of yarn per cardigan

1500 meters per pullover

Explanation:

Answer 2

The machine uses 1575 meters of yarn per cardigan and uses 1500 meters per pullover.

Explanation:

Let P be yarn needed by machine for each pullover and C be yarn needed by machine for each Cardigan.

We are told that the machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans. We can represent this information as:

`20C=21P...(1)`

The machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers. We can represent this information as:

`200P+100C=457,500...(2)`

Let us solve our system of equations using substitution method.

From equation (1) we will get,

`C=(21P)/(20)`

Upon substituting this value in equation (2) we will get,

`200P+100((21P)/(20))=457,500`

`200P+5*21P=457,500`

`200P+105P=457,500`

`305P=457,500`

`P=(457,500)/(305)`

`P=1500`

Therefore, the machine uses 1500 meters of yarn per pullover.

Upon substituting P=1500 in equation (1) we will get,

`20C=21*1500`

`20C=31,500`

`C=(31,500)/(20)`

`C=1575`

Therefore, machine uses 1575 meters of yarn per cardigan.