Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 41 small gifts and 18 large gifts, earning a total of $167. Today, they wrapped 14 small gifts and 26 large gifts, and earned $196. How much did they charge to wrap the gifts?
The organization charges

to wrap a small gift and $4
to wrap a large one.

Answer 1

The organization charges $1 to wrap a small gift and $7 to wrap a large one.

In order to write a system of linear equations to describe this situation, we would assign variables to the cost of small gift and cost of large gift, and then translate the word problem into a linear equation as follows:

• Let the variable x represent the cost of small gift.
• Let the variable y represent the cost of large gift.

Since they wrapped 41 small gifts and 18 large gifts, earning a total of $167, a linear equation that model the situation is given by;

41x + 18y = 167

Additionally, they wrapped 14 small gifts and 26 large gifts, and earned $196;

14x + 26y = 196

By solving the system of equations graphically, we have;

x = $1 for a small gift

y = $7 for a large gift.