Question

A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 39 small gifts and 16 large gifts, earning a total of $277. Today, they wrapped 35 small gifts and 42 large gifts, and earned $525. How much did they charge to wrap the gifts?

Answer 1

The answer is 4 dollars for the small gifts, 10 dollars for the large gifts

Answer 2

The organization charges $3 for wrapping small gifts and $10 for wrapping large gifts.

SOLUTION:

Given, a local service organization is wrapping gifts at the mall to raise money for charity.

Yesterday, they wrapped 39 small gifts and 16 large gifts, earning a total of $277.

Today, they wrapped 35 small gifts and 42 large gifts, and earned $525.

We need to find how much did they charge to wrap the gifts?

Let, the charge for wrapping small gifts be x

And the charge for wrapping large gifts be y

Now, according to the given information,

39x + 16y = 277 ---- (1)

35x + 42y = 525

7(5x + 6y) = 7 x 75

5x + 6y = 75

6y = 75 – 5x

`$2 y=(75-5 x)/(3)$`

On rearranging we get,

`$2 y=25-(5)/(3) x$` --- eqn 2

Now, substitute (2) in (1)

`39 x+8\left(25-(5)/(3) x\right)=277`

`$39 x+200-(40)/(3) x=277$`

117x + 600 – 40x = 831

117x – 40x = 831 – 600

77x = 231

x = 3

Now, substitute x value in (2)

`$2 y=25-(5)/(3)(3)$`

2y = 25 – 5

2y = 20

y = 10

Hence, the organization charges $3 for wrapping small gifts and $10 for wrapping large gifts.