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).
Understand & Think: Do you understand what is being asked and what you need to do? Do you have a list of things you know, ideas to try, and a plan for doing it? Identify the problem and list your strategies.
Problem: Find how much each type of wrapping paper costs per roll algebraically.
Strategies:
1. Write a system of linear equations
2. Solve the system of equations
System of Linear Equations:
Let x = cost of plain wrapping paper per roll
Let y = cost of holiday wrapping paper per roll
2x + y = 43
7x + y = 93
Solve the system of equations:
7x + y = 93
-2x - y = -43
5x = 50
x = 10
Substitute x = 10 into 2x + y = 43
2(10) + y = 43
20 + y = 43
y = 23
Answer:
The cost of plain wrapping paper per roll is $10 and the cost of holiday wrapping paper per roll is $23.
Yes, I understand what is being asked and what needs to be done. We need to find the cost of each type of wrapping paper per roll. To do this, we can set up a system of linear equations based on the given information.
Let's assume that the cost of one roll of plain wrapping paper is P dollars and the cost of one roll of holiday wrapping paper is H dollars.
From the given information, we can set up two equations:
1. Brandy sold 2 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total of $43:
2P + 1H = 43
2. Jennifer sold 7 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total of $93:
7P + 1H = 93
Now, we have a system of two linear equations. The next step is to solve this system to find the values of P and H.
We can solve this system using the method of substitution or elimination. Let's use the method of substitution.
Solve Equation 1 for P:
2P = 43 - 1H
P = (43 - H)/2
Substitute this value of P into Equation 2:
7((43 - H)/2) + H = 93
Multiply through by 2 to eliminate the denominator:
7(43 - H) + 2H = 186
Distribute the 7:
301 - 7H + 2H = 186
Combine like terms:
301 - 5H = 186
Subtract 301 from both sides:
-5H = -115
Divide by -5:
H = 23
Now substitute this value of H back into Equation 1 to find P:
2P + 1(23) = 43
2P = 43 - 23
2P = 20
P = 10
Therefore, the cost of one roll of plain wrapping paper is $10 and the cost of one roll of holiday wrapping paper is $23.
The problem is asking us to find the cost per roll for both plain wrapping paper and holiday wrapping paper. We are given two equations with the quantities sold and the total amount collected by each person.
Let's assign variables to the unknown values:
Let x represent the cost per roll of plain wrapping paper.
Let y represent the cost per roll of holiday wrapping paper.
From Brandy's sales:
2x + 1y = 43
From Jennifer's sales:
7x + 1y = 93
We now have a system of linear equations. We can solve this system algebraically.