Question

A man has 28 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 520 cents, how many dimes and how many quarters does he have?

Answer 1

Assuming x = dimes, y = quarters

$x + y = 28 \\ 0.1x + 0.25y = 5.20$

$x + y = 28 \\ x = 28 - y$

Substitute that into,
$0.1(28 - y) + 0.25y = 5.20 \\ 2.8 - 0.1y + 0.25y = 5.20 \\0.15y = 2.4 \\ y = 16$

Answer : He has 16 quarters.

Hope this helps. - M