Question

Vlad has 9 coins, all quarters and dimes, worth a total of $1.80. This is shown by the system of linear equations, x + y = 9 and 0.25x + 0.1y = 1.8, on the graph.

A coordinate grid showing Vlad's Change with Number of Quarters on the x-axis and Number of Dimes on the y-axis with 2 lines. The first line passes through (0, 18) and (6, 3). The second line passes through (0, 9) and (6, 3).
How many dimes does he have?

3
6
7
9

Answer 1

Let x = quarters and y = dimes. From x + y = 9 and 0.25x + 0.10y = 1.80:

5x + 2y = 36 (multiply money equation by 20).
Substitute x = 9 − y: 5(9 − y) + 2y = 36 → 45 − 3y = 36 → y = 3.

He has 3 dimes.