SOLUTION: Phil has 50 nickels and dimes worth $4.15. How many dimes does he have?

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Question 547301: Phil has 50 nickels and dimes worth $4.15. How many dimes does he have?
Answer by mathie123(224) About Me  (Show Source):
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Let n be the number of nickels and d be the number of dimes that Phil has.
Since each nickel is worth 5 cents, and each dime is worth 10 cents, we have:
5n%2B10d=415 (1)
(Note: we had to use 415 rather than 4.15 since we are counting in cents)
We also know that
n%2Bd=50
n=50-d (2)
Substituting (2) into (1),
5%2850-d%29%2B10d=415
250-5d%2B10d=415
250%2B5d=415
250%2B5d-250=415-250
5d=165
d=33
Now substituting this value of d into (2) we get:
n=50-33
n=17
So Phil has 17 nickels and 33 dimes.