SOLUTION: Vince has 3 times as many nickels as dimes. The coins have a total value of $1.50. How many of each does he have?

Question 251785: Vince has 3 times as many nickels as dimes. The coins have a total value of $1.50. How many of each does he have?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Coin problems require you to keep track of the count of the coins and their values.
n = number of nickels
5n = value of the nickels
d = number of dimes
10d = value of the dimes
.
We are told
5n + 10d = $1.50 = 150 cents.
.
It is best to deal with cents so that everything is in the same units. You could try to work with dollars, but then you'd have 0.05n and 0.10d as the values. To eliminate the decimals, you'd multiply by 100, which means you're just dealing with cents anyway.
.
We also are told "Vince has 3 times as many nickels as dimes." That means:
n = 3d
.
Now substitute what you know and solve the equations.
.
5n + 10d = 150
.
Substitute 3d for n.
5(3d) + 10d = 150
.
Simplify and collect terms.
15d + 10d = 150
25d = 150
.
Divide both sides by 25.
d = 6
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So Vince has 6 dimes.
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Substituting in the value equation, the value of the dimes is 60 cents.
That means the value of the nickels is 90 cents (150 - 60).
At 5 cents each, that means Vince has 90/5 = 18 nickels.
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Checking our work, we know the equations total 150 cents...
10d = 10(6) = 60 cents
5n = 5(18) = 90 cents
Total = 150 cents
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But does he have 3 times as many nickels as dimes?
3d = 3*6 = 18
n = 18
Yes, he does.
.
So our answer is:
Vince has 6 dimes and 18 nickels.
.
Done.
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