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How Many Coins ?

Sam received $13 from his father.
He received 10 more dimes than nickels
and 22 more quarters than dimes.
How many coins of each did he receive?

Let the number of dimes be d.
Let the number of nickels be n.       
Let the number of quarters be q.

Then number of each coin denomination is -

d = d
n = d -10
q = d + 22

And the value of each coin denomination is -

dimes :  10d
nickels :  5(d -10)
quarters : 25(d + 22)
 
Total value of all coins is 1300 cents.

5(d – 10) + 10d + 25(d + 22) = 1300
5d – 50 + 10d + 25d + 550 = 1300
5d + 10d + 25d = 1300 + 50 – 550 
40d = 800
d = 20 is the number of dimes.

nickels = d – 10 = 10
quarters = d + 22 = 42

Therefore Sam received 
10 nickels, 20 dimes and 42 quarters.