SOLUTION: A stationery company sells two types of notepads to college bookstores, the first wholesaling for 40� and the second for 70�. The company receives an order for 570 notepads, togeth

Question 1032006: A stationery company sells two types of notepads to college bookstores, the first wholesaling for 40� and the second for 70�. The company receives an order for 570 notepads, together with a check for $282. If the order fails to specify the number of each type, how should the company fill the order?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Let the number of cheaper notepads be x
Let the number of costlier notepads be y


                       Cost       COST
Type       Number       of         of
 of          of        EACH       ALL
notepad   notepads   notepad    notepads
-------------------------------------------
cheaper      x        $0.40      $0.40x
costlier     y        $0.70      $0.70y
-------------------------------------------
TOTALS     570        -----    $282.00

 The first equation comes from the number of notepads column.

  

                 x + y = 570

 The second equation comes from the last column.
  

           0.40x + 0.70y = 282

Get rid of decimals by multiplying every term by 10:

                 4x + 7y = 2820

 So we have the system of equations:
           .

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

           x + y = 570
               y = 570 - x

Substitute (570 - x) for y in 4x + 7y = 2820

   4x + 7(570 - x) = 2820
    4x + 3990 - 7x = 2820
        -3x + 3990 = 2820
               -3x = -1170
                 x = 390 = the number of cheaper notepads

Substitute in y = 570 - x
              y = 570 - (390)
              y = 180 costlier notepads

Checking:  390 cheaper notepads cost $156.00 and 180 costlier
           notepads costs $126.00
            That's 570 notepads.
            And indeed $156.00 + $126.00 = $282.00
Edwin

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