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: 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 2Now, 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.