SOLUTION: kevin and randy muise have a jar containing 79 coins, all of which are either quarters or nickels. the total value of the coins in the jar is 12.75 How many of each type of coins d

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Question 1025471: kevin and randy muise have a jar containing 79 coins, all of which are either quarters or nickels. the total value of the coins in the jar is 12.75 How many of each type of coins do they have?
Answer by Edwin McCravy(20056) 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       79      -----       $12.75

 The first equation comes from the second 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 = 79

 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 = 12.75

Get rid of decimals by multiplying every term by 100:

           25x + 5y = 1275

 So we have the system of equations:

           system%28x+%2B+y+=+79%2C25x+%2B+5y+=+1275%29.

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

              x + y = 79
                  y = 79 - x
 
Substitute (79 - x) for y in 25x + 5y = 1275

    25x + 5(79 - x) = 1275
     25x + 395 - 5x = 1275
          20x + 395 = 1275
                20x = 880
                  x = 44 = the number of quarters.

Substitute in y = 79 - x
              y = 79 - (44)
              y = 35 nickels.


Checking:  44 quarters is $11.00 and 35 nickels is $1.75
            That's 79 coins.
            And indeed $11.00 + $1.75 = $12.75
Edwin