SOLUTION: A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the nickels were quarters and the quarters were dimes,

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Question 247355: A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75. How many quarters are in the original collection?
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let represent the number of nickels.

Let represent the number of dimes.

Let represent the number of quarters.

So altogether you have



total coins.

Then is the value of the nickels in cents. is the value of the dimes in cents, and is the value of the quarters in cents.

All together, you have



expressed in cents.

But if you had quarters, you would have cents, and if you had nickels, you would have cents, and if you had dimes, you would have cents, and that would all add up to 275 cents, so:



Now you have a system of three equations in three variables to solve. Since the problem only asks for the number of quarters, you really only need solve for , but I would solve for all three variables and plug the values back in to the original equations in order to check my work.


John
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