SOLUTION: Twenty-five coins, whose value is $2.75 are made up of nickels, dimes, and quarters. If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total va

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Question 198518: Twenty-five coins, whose value is $2.75 are made up of nickels, dimes, and quarters. If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total value would be $3.75. How many coins of each type are there?
Answer by Edwin McCravy(20060) About Me  (Show Source):
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Twenty-five coins, whose value is $2.75 are made up of nickels, dimes, and quarters. If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total value would be $3.75. How many coins of each type are there?
Twenty-five coins, 

so we write:

N +   D +   Q =  25

whose value is $2.75 are made up of nickels, dimes, and quarters. 

so we write:

5N + 10D + 25Q = 275

If the nickels were dimes, 

we'd have 10N cents

the dimes were quarters,

we'd have 25D cents

and the quarters were nickels, 

we'd have 5Q cents.

the total value would be $3.75. 

So 10N + 25D + 5Q = 375

So the system is

  N +   D +   Q =  25
 5N + 10D + 25Q = 275
10N + 25D +  5Q = 375

Solve that and get 10 nickels, 10 dimes and 5 quarters.

10 nickels =  50 cents
10 dimes =   100 cents
5 quarters = 125 cents
             ---------
             275 cents or $2.75

If we had

10 dimes =    100 cents
10 quarters = 250 cents
5 nickels =    25 cents
             ---------
              375 cents or $3.75   

So it checks.

Edwin