SOLUTION: A coin purse contains 24 coins in dimes, quarters and half-dollars. There are five more dimes than quarters. The total value of the coins is $5.45. How many dimes are in the coin

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Question 10153: A coin purse contains 24 coins in dimes, quarters and half-dollars. There are five more dimes than quarters. The total value of the coins is $5.45. How many dimes are in the coin purse? I'm thinking it should be set up like 10q+50+25q+50H=545. It doesn't come out right. Where is my mistake here? Also the other part I think is suppose to be d+d+5+h=24. I've worked it 6 different ways and still it doesn't work out. I have a furmula but for some reason following that doesn't help.
Answer by mathmaven53(29) About Me  (Show Source):
You can put this solution on YOUR website!
D is dimes,Q is quarters, H is half dollars
We have D + Q + H = 24
D = Q + 5
The value of the coins is
10D + 25Q + 50H = 545
By the first two equations
2Q +5 + H = 24
1) 2Q + H = 19
By the second and third equations
10(Q+5) + 25Q + 50H = 545
This can be reduced to
2) 7Q + 10H = 99
Solve 1) and 2) for Q
Q = 7
Then D = Q + 5
= 12
By 1) H = 19 - 2Q
= 5
Twelve dimes in purse