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?

Twenty-five coins,

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so we write:

N +   D +   Q =  25
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whose value is $2.75 are made up of nickels, dimes, and quarters. 
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so we write:

5N + 10D + 25Q = 275
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If the nickels were dimes, 
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we'd have 10N cents
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the dimes were quarters,
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we'd have 25D cents
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and the quarters were nickels, 
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we'd have 5Q cents.
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the total value would be $3.75. 
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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</pre>