SOLUTION: a boy has 7 more dimes than quarters. The total value of the coins is $4.90. Find the number of dimes and quarters.

Question 18058: a boy has 7 more dimes than quarters. The total value of the coins is $4.90. Find the number of dimes and quarters.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
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)
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