Question 286116: i need help on this word problem as well. i have the first part but im stuck on the second. The problem is: In Josh's Bank there is a collection on nickles, dimes, and quarters which amount to $3.20. There are 3 times as many quarters as nickles, and 5 more dimes than nickles. How many coins of each type are there? I have the first equation, .5n+.10d+.25q=3.20 but i cant figure out the second part.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! In solving money problems you have to keep track of the counts for the different coins as well as their values.
n = number of nickels
5n = value of the nickels in cents
d = number of dimes
10d = value of the dimes in cents
q = number of quarters
25q = value of quarters in cents
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$3.20 = 320 cents = 5n + 10d + 25q
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It is important to have everything in cents to avoid mismatched dollars and cents.
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q = 3n :: There are 3 times as many quarters as nickels, so you would have multiply n by 3 to be equal.
d = n+5 :: There are 5 more dimes than nickels.
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So, we can substitute what we know into the value equation.
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5n + 10d + 25q = 320
5n + 10(n+5) + 25(3n) = 320
5n + 10n + 50 + 75n = 320
90n = 270
n = 3
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Substituting n=3 we can find d and q.
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d = n+5 = 3+5 = 8
q = 3n = 3*3 = 9
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Check the work by making sure the value of these coin counts is $3.20.
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5n = 5(3) = 15 = $0.15
10d = 10(8) = 80 = $0.80
25q = 25(9) = 225 = $2.25
$0.15+$0.80+$2.25 = $3.20
Correct!
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Answer:
nickels = 3
dimes = 8
quarters = 9
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Done.
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