SOLUTION: Gabby's piggy bank contains nickles and dimes worth $4.05. If she has 59 coins in all, how many of each does she have?

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Question 1031132: Gabby's piggy bank contains nickles and dimes worth $4.05. If she has 59 coins in all, how many of each does she have?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

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


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickles      x      $0.05       $0.05x
dimes        y      $0.10       $0.10y
-------------------------------------------
TOTALS      59      -----       $4.05

 The first equation comes from the number of coins column.

  %28matrix%283%2C1%2CNumber%2Cof%2Cnickles%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 = 59

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickles%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 = 4.05

Get rid of decimals by multiplying every term by 100:

                5x + 10y = 405

 So we have the system of equations:
           system%28x+%2B+y+=+59%2C5x+%2B+10y+=+405%29.

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

                   x + y = 59
                       y = 59 - x

Substitute (59 - x) for y in 5x + 10y = 405

         5x + 10(59 - x) = 405
          5x + 590 - 10x = 405
               -5x + 590 = 405
                     -5x = -185
                       x = 37 = the number of nickles.

Substitute in          y = 59 - x
                       y = 59 - (37)
                       y = 22 dimes.

Checking:  37 nickles is $1.85 and 22 dimes is $2.20
           That's 59 coins.
           And indeed $1.85 + $2.20 = $4.05

Edwin