Question

Sam and Marissa are shopping at the same store. Sam bought 2 model airplanes and 6 toy cars. He paid $17 total. Marissa bought 2 model airplanes and returned 10 toy cars. She paid $9 total. A system of equations that represents their purchases and returns is shown below, where  represents the cost of a model airplane and  represents the cost of a toy car.

2x+6y=17

2x-10y=9
What is the cost of one model airplane?

Answer 1

Subtract the second equation from the first:
(2x+6y) − (2x−10y) = 17 − 9 → 16y = 8 → y = 0.5.

Plug y into 2x + 6y = 17:
2x + 6(0.5) = 17 → 2x + 3 = 17 → 2x = 14 → x = 7.

The model airplane costs $7.