SOLUTION: Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters and nickels. The total value of the coins in the jar is $13.05. How many of each type of coin

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Question 1033019: Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters and nickels. The total value of the coins in the jar is $13.05. How many of each type of coin do they have?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of quarters be x
Let the number of nickels be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters      x      $0.25       $0.25x
nickels       y      $0.05       $0.05y
-------------------------------------------
TOTALS       65      -----      $13.05

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

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

                 x + y = 65

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

           0.25x + 0.05y = 13.05

Get rid of decimals by multiplying every term by 100:

          25x + 5y = 1305

 So we have the system of equations:
           system%28x+%2B+y+=+65%2C25x+%2B+5y+=+1305%29.

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

           x + y = 65
               y = 65 - x

Substitute (65 - x) for y in 25x + 5y = 1305

    25x + 5(65 - x) = 1305
     25x + 325 - 5x = 1305
          20x + 325 = 1305
                20x = 980
                  x = 49 = the number of quarters.

Substitute in y = 65 - x
              y = 65 - (49)
              y = 16 nickels.

Checking:  49 quarters is $12.25 and 16 nickels is $0.80
            That's 65 coins.
            And indeed $12.25 + $0.80 = $13.05
Edwin