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).
Part A: What is being asked in the problem and what does that mean? What plan am I going to try?
Part B: Then, solve.
Part A: In this problem, we are being asked to find the cost per roll for both plain wrapping paper and holiday wrapping paper. To do this, we can use a system of linear equations to represent the total amounts and costs of the wrapping paper sold by both Brandy and Jennifer.
Part B: Let's denote the cost per roll of plain wrapping paper as P, and the cost per roll of holiday wrapping paper as H.
From the information given, we can set up the following system of equations:
2P + 1H = 43 (equation 1) (representing Brandy's sales)
7P + 1H = 93 (equation 2) (representing Jennifer's sales)
To solve this system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method:
Multiply equation 1 by 7 and equation 2 by 2 to make the coefficients of H in both equations the same:
14P + 7H = 301 (equation 3)
14P + 2H = 186 (equation 4)
Now, subtract equation 4 from equation 3 to eliminate P:
14P - 14P + 7H - 2H = 301 - 186
5H = 115
Divide both sides by 5 to solve for H:
H = 23
Substitute this back into equation 1 to solve for P:
2P + 1(23) = 43
2P + 23 = 43
2P = 20
P = 10
Therefore, the cost per roll of plain wrapping paper is $10, and the cost per roll of holiday wrapping paper is $23.