SOLUTION: A collection of 36 coins consist of dimes and nickles. The total value is $2.15. How many dimes are there

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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
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
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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