Question

Brandy and Jennifer are selling wrapping paper for a school fundraiser.

Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Brandy sold 2 rolls
of plain wrapping paper and 1 roll of holiday wrapping paper for a total of $43. Jennifer sold 7 rolls of plain
wrapping paper and 1 roll of holiday wrapping paper for a total of $93. Write a system of Linear Equations
and find how much each type of wrapping paper costs per roll algebraically (Not graphing).

Answer 1

The cost of each roll of plain wrapping paper is $10 and the cost of each roll of holiday wrapping paper is $23.

Step-by-step explanation:

Let's assume that the cost of each roll of plain wrapping paper is x dollars and the cost of each roll of holiday wrapping paper is y dollars.

According to the given information, Brandy sold 2 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total of $43. This can be represented by the equation 2x + y = 43.

Similarly, Jennifer sold 7 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total of $93. This can be represented by the equation 7x + y = 93.

We now have a system of linear equations:

2x + y = 43

7x + y = 93

To solve the system algebraically, we can use the method of substitution or elimination. Let's use elimination:

Subtracting the first equation from the second equation, we get:

7x + y - (2x + y) = 93 - 43

5x = 50

x = 10

Substituting the value of x into one of the original equations, we can find the value of y:

2(10) + y = 43

y = 23

Therefore, the cost of each roll of plain wrapping paper is $10 and the cost of each roll of holiday wrapping paper is $23.