Question 60618
Let Joe have x dimes and y quarters.
Then x + y = 479 ---------(1)  [since he had 479 coins]

Value of x dimes = 10x cents
Value of y quarters = 25y cents

Total value = 10x  + 25y

==> 10x + 25y = 7250 cents [he totally had $72.50]
==> 10x + 25y = 7250 ------------------(2)

Multiplying (1) by 10 we get..
10x + 10y = 4790
10x + 25y = 7250 --------(2)

Subtracting the above two equations, we get
- 15y = -2460
==> -15y/-15 = -2460/-15
==> y = 164
Plugging in this value in (1) ,
x + 164 = 479
==> x = 479 - 164 [Subtracting 164 from both the sides ]
==> x = 315

So Joe had 315 dimes and 164 quarters.