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

Question

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. Solve the system algebraically (not by graphing).

Answer 1

Let \( p \) represent the cost of a roll of plain wrapping paper, and let \( h \) represent the cost of a roll of holiday wrapping paper. Based on the sales information provided, we can set up the following system of linear equations:

1. From Brandy's sales: \[ 2p + 1h = 43 \tag{1} \]

2. From Jennifer's sales: \[ 7p + 1h = 93 \tag{2} \]

Now we will solve this system algebraically. We can start by isolating \( h \) in equation (1):

\[ h = 43 - 2p \tag{3} \]

Next, we substitute equation (3) into equation (2):

\[ 7p + (43 - 2p) = 93 \]

Simplifying this equation gives:

\[ 7p + 43 - 2p = 93 \]

Combining like terms:

\[ 5p + 43 = 93 \]

Subtracting 43 from both sides:

\[ 5p = 93 - 43 \]

\[ 5p = 50 \]

Dividing both sides by 5:

\[ p = 10 \]

Now that we have the cost of plain wrapping paper, we can substitute \( p = 10 \) back into equation (3) to find \( h \):

\[ h = 43 - 2(10) \]

\[ h = 43 - 20 \]

\[ h = 23 \]

Thus, the costs per roll of wrapping paper are:

• \( p = 10 \) (cost of plain wrapping paper)
• \( h = 23 \) (cost of holiday wrapping paper)

In summary:

• The cost of a roll of plain wrapping paper is $10.
• The cost of a roll of holiday wrapping paper is $23.