SOLUTION: A cashier has a total of 90 bills,made up of fives and tens. The totL value of the money is 645. How many of each kind does he have.

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Question 1027190: A cashier has a total of 90 bills,made up of fives and tens. The totL value of the money is 645. How many of each kind does he have.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Let the number of fives be x
Let the number of tens be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
bill        bills      bill      bills
-------------------------------------------
fives        x          $5       $5x
tens         y         $10      $10y
-------------------------------------------
TOTALS      90        -----     $645

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2Cfives%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Ctens%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cbills%29%29

                 x + y = 90

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

           5x + 10y = 645

 So we have the system of equations:
           system%28x+%2B+y+=+90%2C5x+%2B+10y+=+645%29.

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

           x + y = 90
               y = 90 - x

Substitute (90 - x) for y in 5x + 10y = 645

   5x + 10(90 - x) = 645
    5x + 900 - 10x = 645
         -5x + 900 = 645
               -5x = -255
                 x = 51 = the number of fives.

Substitute in y = 90 - x
              y = 90 - (51)
              y = 39 tens.

Checking:  51 fives is $255 and 39 tens is $390
            That's 90 bills.
            And indeed $255 + $390 = $645
Edwin