Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Mrs. Copeland's grandchildren are participating in a gift wrap sale to raise money for their school. She decided to stock up, so she ordered 4 rolls of reversible paper and 2 rolls of metallic paper from Melissa, spending a total of $68. She also ordered 1 roll of reversible paper and 4 rolls of metallic paper from Xavier, which cost a total of $52. Assuming that rolls of each type are priced the same, what is the price for each kind of paper?

Answer 1

Given that,

Mrs. Copeland's grandchildren are participating in a gift wrap sale

she ordered 4 rolls of reversible paper and 2 rolls of metallic paper from Melissa, spending a total of $68.

She also ordered 1 roll of reversible paper and 4 rolls of metallic paper from Xavier, which cost a total of $52.

Let x be the price of a roll of reversible paper and y be the price of a roll of metallic paper.

we get, the system of equations as,

`4x+2y=68-----(1)`
`1x+4y=52------(2)`

multiply the equation (2) by 4 we get,

`4x+16y=208-----(3)`

Subtract equation (1) from equation (3) we get

`4x+16y-4x-2y=208-68`
`14y=140`
`y=10`

Substitute y=10 in the equation (1) we get,

`4x+2(10)=68`
`4x+20=68`
`4x=68-20`
`4x=48`
`x=12`

The price of a roll of reversible paper is $12

The price of a roll of metallic paper is $10

Answer is:

The price of a roll of reversible paper is $12

The price of a roll of metallic paper is $10