SOLUTION: Daniel has $2.90 in nickels, dimes and quarters. If he has three more nickels than dimes and twice as many dimes as quarters, how many of each does he have?

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Question 597476: Daniel has $2.90 in nickels, dimes and quarters. If he has three more nickels than dimes and twice as many dimes as quarters, how many of each does he have?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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[I] Define your variables
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n = the number of nickels
d = the number of dimes
q = the number of quarters
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[II] Create equations showing the given relationships
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There are three more nickels than dimes.
n=d%2B3
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There are twice as many dimes as quarters.
d=2q or q=d%2F2
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The total amount of money is $2.90
The value of the nickels is $0.05 times the number of nickels, or 0.05n
The value of the dimes is $0.10 times the number of dimes, or 0.10d
The value of the quarters is $0.25 times the number of quarters, or 0.25q
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0.05n%2B0.10d%2B0.25q=2.90
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[III] Solve the system of equations.
I'll use the substitution method.
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Substitute d+3 for n and d/2 for q into the value equation.
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0.05n%2B0.10d%2B0.25q=2.90
0.05%28d%2B3%29%2B0.10d%2B0.25%28d%2F2%29=2.90
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Simplify and solve for d.
0.05d%2B0.15%2B0.10d%2B0.125d=2.90
0.275d%2B0.15=2.90
0.275d=2.75
d=10
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The equation d=10 means that there are 10 dimes.
There are n = d+3 = 10+3 = 13 nickels.
There are d/2 = 10/2 = 5 quarters.
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[IV] Check your work.
Do these coins add up to $2.90?
13 nickels is 6*13 = $0.65
10 dimes is 10*10 = $1.00
5 quarters is 5*25 = $1.25
$0.65 + 1.00 + 1.25 = $2.90
Check!
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That's it!
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Feel free to email me via gmail if the explanation is unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com