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Question

A collection of 70 coins consisting of dimes, quarters, and half-dollars has a value of $17.75. There are 3 times as many quarters as dimes. Find the number of each kind of coin.

Someone pleas show me how to set this up and get the answer! I have tried several different ways, but get stuck. I know the answers are 15 dimes, 45 quarters, and 10 half-dollars - but I don't know how to figure that out.

I start setting it up like x+3x=70, but I get confused because of the half-dollars not being there to set up the equation. Please help!!

If someone could please show me how to set up and answer this, I'd appreciate it - for some reason, this one is just stumping me!!!

Answer 1

I think you need a system of equations. Try:

x+3x+y=70

.10(x)+.25(3x)+.50(y)=17.75

Answer 2

let d q and h be how many of each coin you have

10d + 25q + 50h = 1775

also

3d = q

so

10d + 25(3d) + 50h = 1775

85d + 50h = 1775  (***)

You also know that d + q + h = 70

d + 3d + h = 70

4d + h = 70

h = 70 - 4d

Plug this into the other equation (***)

85d + 50(70 - 4d) = 1775

and solve

85d + 3500 - 200d = 1775

200d  - 85d = 3500 - 1775

115d = 1725

d = 1725 / 115

d = 15

since there are 3 times as many quarters as dimes there are 45 quarters

and since there are 70 coins in total there are 10 half dollars