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) (Show Source): You can put this solution on YOUR website!
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:
Eqn 2:
Eqn 3:
We then need to isolate two of the variables. I will choose to isolate for d in Eqn 3:
And q in Eqn 1:
Now substitute the value of d = 2.5n into Eqn 1:
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:
Distributing:
Collecting like terms:
{{0.3n-0.875n=12.60-5.60}}}
Divide both sides by 0.575:
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.
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