Help with a Math word problem please!?

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!!

Answer 1

d = number of dimes

q = number of quarters

h = number of half-dollars

You have three variables - you need three equations.

First Equation (number of dimes plus quarters plus half dollars adds to 70)

d + q + h = 70 (there are 70 coins)

Second Equation

q = 3*d (there are three times as many quarters as dimes)

Third Equation (you have 17.75 dollars)

d*(0.10) + q*(0.25) + h*(0.50) = $17.75

(dime is worth 0.10 dollars; quarter is worth 0.25 dollars; half dollar is worth 0.50 dollars).

You can solve that any way you like.