# If evan has 10 dimes and quarters in his pocket, and they have combined value of 190 cents, how many of each coin does he have?

Oct 24, 2016

6 quarters and 4 dimes.

#### Explanation:

To solve this problem in two variables (dimes and quarters) it is necessary to write two equations.

The first equation is dimes + quarters = $10$

The second equation is $0.10$ x dimes + $0.25$ x quarters =$1.90 Now it is clear then dimes = $10$- quarters so this value can be put into the second equation giving $0.10 \times$( 10 - quarters) + $0.25 \times$quarters = $ 1.90

$1.90 = 190 cents. This gives $100$cent - $10$quarters + $25$quarters = $190$cents Now $25$quarters - $10$quarters = $15$quarters. so $15 q u a r t e r s +$100$c e n t s =$190 cents now subtract $100$cents from both sides $15$quarters + $100$cents - $100$cents = $190$cents - $100$cents giving $15$quarters = $90$cents. It takes 6 quarters If there are $6$quarters there must be only $4$dimes $6 + 4 = 10$$90$cents = $0.90$$\left(\frac{0.90}{.15}\right) \times \left(\frac{100}{100}\right) = \frac{90}{15} = 6$$6$quarters x $0.25 /quarter = $1.50 $4$dimes x $0.10 /dime = $0.40# $$ Total =$1.90