SOLUTION: 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

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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?
Answer by dabanfield(803) About Me  (Show Source):
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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.