SOLUTION: If Cesar has 17 nickels and quarters in his pocket, and they have a combined value of 265 cents, how many of each coin does he have ?

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Question 1025173: If Cesar has 17 nickels and quarters in his pocket, and they have a combined value of 265 cents, how many of each coin does he have ?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

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


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels        x      $0.05       $0.05x
quarters       y      $0.25       $0.25y
-------------------------------------------
TOTALS        17      -----       $2.65

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2Cnickels%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29
            
                   x + y = 17

 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%2Cquarters%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

           0.05x + 0.25y = 2.65

Get rid of decimals by multiplying every term by 100:

                5x + 25y = 265

 So we have the system of equations:
           system%28x+%2B+y+=+17%2C5x+%2B+25y+=+265%29.

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

           x + y = 17
               y = 17 - x

Substitute (17 - x) for y in 5x + 25y = 265

     5x + 25(17 - x) = 265
      5x + 425 - 25x = 265
          -20x + 425 = 265
                -20x = -160
                   x = 8 = the number of nickels.

Substitute in y = 17 - x
              y = 17 - (8
              y = 9 quarters.


Checking:  8 nickels is $0.40 and 9 quarters is $2.25
            That's 17 coins.
            And indeed $0.40 + $2.25 = $2.65
Edwin