Chapter 3.1, Problem 69SR

To determine

Find the numbers of each kind of gift wrap were sold.

Answer to Problem 69SR

Number of gift wraps sold was 270 and the number of print wraps sold was 210.

Explanation of Solution

Given:

The Madison High School Marching Band solid − color gift wrap for $4 and print wrap for $6. The total number of rolls sold was 480 and the total amount of money collected was $2340.

Concept Used:

We are told that the total number of rolls sold is 480.

Let the number of gift wrap for $4 = s and the number of printed gift wrap = p

The first equation: $s+p=480$

We are also told that the solid color at 4 dollars per roll and the print at 6 dollars per roll together brought in 2340 dollars.

2^nd equation: $4s+6p=2340$

Solve the first equation for s and plug the result in for s in the second equation.

Distribute the 4, add like terms, subtract 1920 from each side and divide by 2 to solve for p.

Plug p back into the first equation to solve for s.

Calculation:

We are told that the total number of rolls sold is 480.

Let the number of gift wrap for $4 = s and the number of printed gift wrap = p

The first equation: $s+p=480$

We are also told that the solid color at 4 dollars per roll and the print at 6 dollars per roll together brought in 2340 dollars.

2^nd equation: $4s+6p=2340$

  $\begin{array}{l}s+p=\mathrm{480.................}\text{equation}\text{1}\\ s=480-p\mathrm{.................}\text{equation}\text{2}\\ 4s+6p=2340\\ 4(480-p)+6p=2340[\text{plugi}\text{in}s=480-p\text{from}\text{equation}\text{no}\text{2]}\\ 1920-4p+6p=2340\\ 2p+1920=2340\\ 2p+1920-1920=240-1920\text{[}\text{Subtract}1920\text{from}\text{both}\text{sides}\text{]}\\ 2p=420\\ \frac{2p}{2}=\frac{420}{2}[\text{Divide}\text{each}\text{side}\text{by}2]\\ p=210\\ s=480-210=270\end{array}$

Number of gift wraps sold was 270 and the number of print wraps sold was 210.

Thus, the number of gift wraps sold was 270 and the number of print wraps sold was 210.