ANSWER:
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
[tex]$2 y=\frac{75-5 x}{3}$[/tex]
On rearranging we get,
[tex]$2 y=25-\frac{5}{3} x$[/tex] --- eqn 2
Now, substitute (2) in (1)
[tex]39 x+8\left(25-\frac{5}{3} x\right)=277[/tex]
[tex]$39 x+200-\frac{40}{3} x=277$[/tex]
117x + 600 – 40x = 831
117x – 40x = 831 – 600
77x = 231
x = 3
Now, substitute x value in (2)
[tex]$2 y=25-\frac{5}{3}(3)$[/tex]
2y = 25 – 5
2y = 20
y = 10
Hence, the organization charges $3 for wrapping small gifts and $10 for wrapping large gifts.
