Question 725740: A collection of 36 coins consist of dimes and nickles. The total value is $2.15. How many dimes are there Found 2 solutions by nshah11, Edwin McCravy:Answer by nshah11(47) (Show Source):
You can put this solution on YOUR website! 0.05(x) + 0.10(36 - x) = 2.15
-0.05(x) + 3.6 = 2.15
-0.05(x) = -1.45
x = 29 nickels
36 - x = 7 dimes
Two ways to do it.
Without algebra:
It would take $2.15÷$0.05 = 43 nickels to make $2.15. We
start with 43 nickels. But that is 43-36 or 7 coins too many.
So we take away 7 nickels leaving 36 nickels. Now to make up
for those 7 nickels we took away, we replace 7 of those 36
nickels by dimes. So we have 7 dimes and 36-7 or 29 nickels.
With algebra:
Let x = the number of dimes.
Then the number of nickels is 36-x.
coins value per coin value of coins
dimes x 0.10 0.10x
nickels 36-x 0.05 0.05(36-x)
----------------------------------------------------
total 36 2.15
0.10x + 0.05(36-x) = 2.15
Multiply through by 100
10x + 5(36-x) = 215
10x + 180 - 5x = 215
5x + 180 = 215
5x = 35
x =
x = 7
So there are 7 dimes and 36-7 or 29 nickels.
Edwin
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