Your friend claims that she has a bag of 30 coins containing nickels, dimes, and quarters. The total value of the 30 coins is $3. There are twice as many
nickels as there are dimes. Is your friend correct?

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  No

Step-by-step explanation:

If all 30 coins were nickels and dimes, there would be 10 dimes and 20 nickels, for a total value of $2.00. Trading a dime and 2 nickels for an equal number of quarters raises the value to $2.00 -0.10 -2(0.05) +3(0.25) = $2.55.

That is, each such trade adds $0.55 in value to the total amount. Since the original difference of $3.00 -$2.00 = $1.00 is not evenly divisible by $0.55, there cannot be twice as many nickels as dimes.

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For 30 coins, possible numbers of {nickels, dimes, quarters} are ...

{21,2,7}, {18,6,6}, {15,10,5}, {12,14,4}, {9,18,3}, {6,22,2}, {3,26,1}, {30 dimes}

Note that we can have 1.5, 3, or 10.5 times as many nickels as dimes, but not 2 times as many.

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