SOLUTION: A collection of 34 coins consisting of dimes and quarters has a value of $5.50. how many of each type of coin is there?

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Question 157712: A collection of 34 coins consisting of dimes and quarters has a value of $5.50.
how many of each type of coin is there?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
D%2BQ=34coins -------------------------> eqn 1
In eqn 1, we get D=34-Q -------------> eqn 2
Also,
0.10D%2B0.25Q=5.50 --------------------> eqn 3
Substitute eqn 2 in eqn 3:
0.10%2834-Q%29%2B0.25Q=5.50
3.4-0.10Q%2B0.25Q=5.50
0.15Q=5.50-3.40=2.10
cross%280.15%29Q%2Fcross%280.15%29=cross%282.10%2914%2Fcross%280.15%29
Q=14coins ---------> no. of Quarters
Go back eqn 2:
D=34-14=20 --------> no. of Dimes
in doubt? go back eqn 3:
0.10%2820%29%2B0.25%2814%29=5.50
2.00%2B3.50=5.50
5.50=5.50
Thank you,
Jojo