Question 461089: Aviva has a total of 57 coins, all of which are either dimes or nickels. The total value of the coins is $4.65. Find the number of each type of coin.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! With coin problems you have to keep track of the number of coins and of their value.
For example,
d = number of dimes
10d = value of the dimes in cents
n = number of nickels
5n = value of the nickels in cents
.
Given
Aviva has $4.65, which is 465 cents.
Aviva has only nickels and dimes, so we can restate the value.
5n + 10d = 465
Aviva has 57 coins in total.
n + d = 57
.
So we can treat these as a system of equations.
.
5n + 10d = 465
n + d = 57
Multiply the second equation by 5
.
5n + 10d = 465
5n + 5d = 285
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Subtract the second equation from the first equation
5d = 180
Divide both sides by 5
d = 36
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Substitute
n + d = 57
n +36 = 57
n = 57-36
n = 21
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Check to see if this is right.
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5n = 5*21 = 105
10d = 10*36 = 365
105+365 = 465
which is the right answer
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Of course, you could have solved using substitution.
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5n + 10d = 465
n + d = 57
n = 57-d
5(57-d) +10d = 465
285 -5d + 10d = 465
As you can see, you get to the same answer, just in a different way.
.
Done.
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