SOLUTION: In a bag, there are some nickels and dimes. If there are 79 coins together and the total amount of money is $6, find the number of dimes.

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Question 1108361: In a bag, there are some nickels and dimes. If there are 79 coins together and the total amount of money is $6, find the number of dimes.
Answer by greenestamps(13203) (Show Source):
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If all 79 coins were dimes, the total value would be $7.90; but it is only $6.00. With all dimes, the total value is $1.90 too much.

Each time we replace a dime with a nickel, the number of coins stays the same but the total value goes down by 5 cents.

To get the total down to the required $6.00, the number of times we need to replace a dime with a nickel is .

That means we end up with 38 nickels; the number of dimes we have left is 79-38 = 41.

Answer: 41 dimes, 38 nickels.

Algebraically....

Let d = number of dimes
Let n = number of nickels
Then
the total number of coins is 79
the total value of the coins (in cents) is 600

Multiply the first equation by 5 and subtract from the second equation to eliminate n:

The number of dimes is 41; then the number of nickels is 79-41 = 38.