word problem

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word problem

There were 35 nickels, dimes, and quarters in all, and their value was $5.00. How many coins of each type were there if there were 2 times as many quarters as nickels?
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Re: word problem

x = # of nickels
2x = # of quarters
35 - 3x = # of dimes   ← total coins is 35

0.05x + 0.25(2x) + 0.1(35 - 3x) = 5   ← value of coin times number of coins equals total value
0.05x + 0.5x + 3.5 - 0.3x = 5   ← distributive property
0.25x + 3.5 = 5   ← combined like terms
0.25x = 1.5   ← subtracted 3.5
x = 6
2x = 12
35 - 3x = 17

6 nickels, 12 quarters, and 17 dimes

- Proof