jmc

Question

While on her vacation in Cancun, Colleen can buy a sombrero and a pair of flip-flops for 32. She can buy the pair of flip-flops and sunglasses for 42. She can buy the sombrero and the sunglasses for 30$. How many dollars does the sombrero cost?

Accepted Answer

Let x, y and z be the prices of a sombrero, a pair of flip-flops and sunglasses, respectively. We can then rewrite the problem as a system of equations: align* x+y &= 32 y+z &= 42 x+z &= 30 align* Adding these gives: align* 2x+2y+2z &= 32+42+30 = 104 x+y+z &= 52 align* So x = (x+y+z)-(y+z) = 52-42=10. So the sombrero costs 10.