Question 249005
Alice has $5.00 in dimes, quarters, and half-dollars. She finds that she has 30 coins altogether and there are four times as many quarters as there are half-dollars. How many dimes does Alice have?

Let x be the number of dimes.
Let y be the number of half-dollars.
Then 4*y is the number of quarters.

Since there are 30 coins we have:

x + y + 4*y = 30 or
(1.) x + 5*y = 30
Note: x = 30 - 5*y

Also since the value of the coins is 5.00 we have:

10*x + 50*y + 4*y*25 = 500 or
10*x + 50*y + 100*y = 500
(2.) 10*x + 150*y = 500

Solve the two equations (1.) and (2.) simultaneously.

Hint:  Substitute 30 - 5*y for x in equation (2.) and then solve for y.