Question

Eugene and Jill are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Eugene sold 3 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for a total of $168. Jill sold 10 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for a total of $252. What is the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper?

Answer 1

The cost of one roll of plain wrapping paper and one roll of shiny wrapping paper is $12 each. This was determined by setting up a system of equations based on the sales made by Eugene and Jill and solving for the prices.

Step-by-step explanation:

To find the cost of one roll of plain wrapping paper and one roll of shiny wrapping paper, we can set up a system of equations based on the information given about Eugene's and Jill's sales:

• Eugene sold 3 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for $168.
• Jill sold 10 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for $252.

Let's define two variables:

We can then write two equations:

1. 3x + 11y = 168 (Eugene's sales)
2. 10x + 11y = 252 (Jill's sales)

To solve for x and y, we can subtract the first equation from the second equation to eliminate y:

10x + 11y - (3x + 11y) = 252 - 168

7x = 84

x = 12

Now that we have the cost of one roll of plain wrapping paper ($12), we can substitute it back into either equation to find y, the cost of one roll of shiny wrapping paper. Let's use the first equation:

3(12) + 11y = 168

36 + 11y = 168

11y = 132

y = 12

Thus, one roll of plain wrapping paper costs $12 and one roll of shiny wrapping paper also costs $12.

Answer 2

let p = cost of 1 plain wrapping paper

let h = cost of 1 shiny rolls wrapping paper

Write an equation for each statement,

" Eugene sold 3 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for a total of $168 "

3p + 11h = $168

Jill sold 10 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for a total of $252."

10p + 11h = $252

Use elimination here,

10p + 11h = $252

3p + 11h = $168

subtraction eliminates h, find p

7p = $84

p = 84/7

p = $12 for wrap of plain paper

Find h using the 1st original equation

3(12) + 11h = 168

36+ 11h = 168

11h = 168 - 36

11h = 132

h = 132/11

h = $12 for shiny wrapping paper

Therefore each plain wrapping paper costs $12 and each shiny wrapping paper costs same $12 !