Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 27 small gifts and 21 large gifts, earning a total of $264. Today, they wrapped 23 small gifts and 21 large gifts, and earned $256. How much did they charge to wrap the gifts?

Answer 1

The organization charges $2 to wrap a small gift and $10 to wrap a large gift.

Step-by-step explanation:

To write a system of equations to describe the situation, we can let x represent the cost of wrapping a small gift and y represent the cost of wrapping a large gift.

From the information given, we can set up the following equations:

27x + 21y = 264

23x + 21y = 256

To solve this system using elimination, we can subtract the second equation from the first equation:

(27x + 21y) - (23x + 21y) = 264 - 256

4x = 8

x = 2

Substituting this value back into either of the original equations, we can solve for y:

27(2) + 21y = 264

54 + 21y = 264

21y = 210

y = 10

Therefore, they charge $2 to wrap a small gift and $10 to wrap a large gift.