# A man has 34 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 565 cents, how many dimes and how many quarters does he have?

Apr 19, 2018

$19$ dimes and $15$ quarters.

#### Explanation:

$34 = x + y$
$34 - x = y$

$565 = 10 x + 25 y$

Substitute the first equation, so

$565 = 10 x + 25 \left(34 - x\right)$

$565 = 10 x + 850 - 25 x$

$15 x = 285$

$x = \text{19 dimes}$

Therefore

$34 - 19 = \text{15 quarters}$