How many Dimes and Quarters

Julian has 22 coins in his pocket, all of which are dimes and quarters. If the total value of

his change is 310 cents, how many dimes and how many quarters does he have?

Julian has 16 dimes and 6 quarters

Step-by-step explanation:

Let's suppose Julian has q quarters and d dimes

The total coins are 22, that is

q+d=22

q=22-d [1]

The total amount of money he has is 310 cents which are made of 10d dimes and 25q quarters

10d+25q=310

Simplifying by 5

2d+5q=62

Using the relation [1]

2d+5 (22-d) = 62

2d+110-5d=62

3d=48 = > d=16

q=22-16 = 6

So Julian has 16 dimes and 6 quarters