SOLUTION: A piggy bank contains 50 coins, all of them nickels, dimes, or quarters. The total value of the coins is $5.60, and the value of the dimes is five times the value of the nickels. H

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Question 238040: A piggy bank contains 50 coins, all of them nickels, dimes, or quarters. The total value of the coins is $5.60, and the value of the dimes is five times the value of the nickels. How many coins of each type are there?
Answer by texttutoring(324) About Me  (Show Source):
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Let n= number of nickels
d= number of dimes
q=number of quarters
We have 3 unknowns, so we need to make 3 equations from the given information.
Eqn 1: n+%2B+d+%2B+q=50
Eqn 2: 0.05%2An%2B0.10%2Ad+%2B+0.25%2Aq=5.60
Eqn 3: 0.10%2Ad=5%2A0.05%2An
We then need to isolate two of the variables. I will choose to isolate for d in Eqn 3:
0.10%2Ad=5%2A0.05%2An
d=5%2A0.05%2An%2F0.10
d=2.5n
And q in Eqn 1:
n+%2B+d+%2B+q+=+50
q=50+-+n+-+d
Now substitute the value of d = 2.5n into Eqn 1:
q=50+-+n+-+2.5n
q=50+-+3.5n
Now we have d in terms of n (d=2.5n), and q in terms of n (q=50-3.5n).
We can now substitute these into Eqn 2:
Eqn 2:
0.05%2An%2B0.10%2Ad+%2B+0.25%2Aq+=+5.60
0.05%2An%2B0.10%2A%282.5n%29+%2B+0.25%2A%2850-3.5n%29=5.60
Distributing:
0.05%2An%2B0.25n%29+%2B+12.5-0.875n=5.60
Collecting like terms:
{{0.3n-0.875n=12.60-5.60}}}
0.575n=6.9
Divide both sides by 0.575:
n=12
We can then use this to find d:
d=2.5n
d=2.5(12)
d=30
We can also now find q:
q=50-3.5n
q=50-3.5(12)
q=50-42
q=8
So there are 12 nickels, 30 dimes, and 8 quarters.