Question

Amanda and Molly are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Amanda sold 3 rolls of plain wrapping paper and 3 rolls of shiny wrapping paper for a total of $60. Molly sold 1 roll of plain wrapping paper and 9 rolls of shiny wrapping paper for a total of $132. What is the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper? (no links please)

Answer 1

Explanation:

Solving system of symultaneous equation:

Let the cost of one roll of plain wrapping pair = x

Let the cost of one shiny wrapping paper = y

Amanda:

Cost of 3 rolls of plain paper + cost of 3 rolls of shiny paper = $ 60

3*x + 3*y = 60

3x + 3y = 60 ------------------(I)

Molly:

Cost of 1 roll of plain paper + cost of 9 rolls of shiny paper = $ 132

x + 9y = 132 ---------------------(II)

x = 132 - 9y ---------------(III)

Substitute x = 132 -9y in equation (I)

3*(132-9y) + 3y = 60

3*132 - 3*9y + 3y = 60

396 - 27y + 3y = 60

Combine like terms

396 - 24y = 60

Subtract 396 from both sides

-24y = 60 - 396

-24y = -336

Divide both sides by (-24)

y = -336/(-24)

`\sf \boxed{y=14}`

Now, substitue y = 14 in equation (III)

x = 132 - 9*14

= 132 - 126

`\sf \boxed{x = 6}`

cost of one roll of plain wrapping paper = $ 6

Cost of one roll of shiny wrapping paper = $ 14