SOLUTION: angelina has collection of nickels and dimes worth &4.65. if she has 70 nickels and dimes, how many of each does she have?

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Question 1034899: angelina has collection of nickels and dimes worth &4.65. if she has 70 nickels and dimes, how many of each does she have?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Let the number of nickels be x
Let the number of dimes be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x      $0.05       $0.05x
dimes        y      $0.10       $0.10y
-------------------------------------------
TOTALS      70      -----       $4.65

 The first equation comes from the "number of coins" column.

  %28matrix%283%2C1%2CNumber%2Cof%2Cnickels%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cdimes%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29 

                   x + y = 70

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cdimes%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

           0.05x + 0.10y = 4.65

Get rid of decimals by multiplying every term by 100:

                5x + 10y = 465

 So we have the system of equations:
           system%28x+%2B+y+=+70%2C5x+%2B+10y+=+465%29.

We solve by substitution.  Solve the first equation for y:

                  x + y = 70
                      y = 70 - x

Substitute (70 - x) for y in 5x + 10y = 465

        5x + 10(70 - x) = 465
         5x + 700 - 10x = 465
              -5x + 700 = 465
                    -5x = -235
                 x = 47 = the number of nickels.

Substitute in y = 70 - x
              y = 70 - (47)
              y = 23 dimes.

Checking:  47 nickels is $2.35 and 23 dimes is $2.30
            That's 70 coins.
            And indeed $2.35 + $2.30 = $4.65
Edwin