You have 35 coins, consisting of nickels, dimes, and quarters. The value of the coins is $4.15. You also know that you have twice as many dimes as quarters. Find the number of each type of coin.
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Value of the coins:
nickel = $0.05
dimes = $0.10
quarter = $0.25
Define x:
Let x be the number of quarter
Dimes = 2x
Nickels = 35 - 2x - x = 35 - 3x
Solve x:
Total amount is $4.15
0.25x + 0.1(2x) + 0.05(35 - 3x) = 4.15
0.25x + 0.2x + 1.75 - 0.15x = 4.15
0.3x = 2.4
x = 8
Find the coins:
quarter = x = 8
dimes = 2x = 2(8) = 16
nickel = 35 - 3x = 35 - 3(8) = 11
Answer: There are 8 quarters, 16 dimes and 11 nickels
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