Question 60618: Joe has been collecting dimes and quarters all year. Now he wants to buy a present for his wife, so he opens his piggy bank. He has 479 coins. When the bank puts them through its counting machine, it tells him he has $72.50. How many dimes and how many quarters does he have?
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! Let Joe have x dimes and y quarters.
Then x + y = 479 ---------(1) [since he had 479 coins]
Value of x dimes = 10x cents
Value of y quarters = 25y cents
Total value = 10x + 25y
==> 10x + 25y = 7250 cents [he totally had $72.50]
==> 10x + 25y = 7250 ------------------(2)
Multiplying (1) by 10 we get..
10x + 10y = 4790
10x + 25y = 7250 --------(2)
Subtracting the above two equations, we get
- 15y = -2460
==> -15y/-15 = -2460/-15
==> y = 164
Plugging in this value in (1) ,
x + 164 = 479
==> x = 479 - 164 [Subtracting 164 from both the sides ]
==> x = 315
So Joe had 315 dimes and 164 quarters.
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