Question 18058
q = number of quarters
d = number of dimes

subtracting 7 from the number of dimes gives the number of quarters

q = d-7

value of the quarters in cents is 25q
value of the dimes in cents is 10d

total value of the coins is 490 cents, so:
25q + 10d = 490

I said:
q = d-7

add 7 to both sides:
d = q+7

substituting:
25q + 10( q+7 ) = 490
25q + 10q + 70 = 490

solving:
35q = 420
q = 420/35
q = 12

d = q+7  (already known)

substituting:
d = 12 + 7
d = 19

so, there are 12 quarters and 19 dimes.
substituting back into our equations:

q = d-7
12 = 19-7  (checks)

25q + 10d = 490
25(12) + 10(19) =490  (checks)