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

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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.

  %28matrix%284%2C1%2CNumber%2Cof%2Ccheaper%2C+notepads%29%29%22%22%2B%22%22%28matrix%284%2C1%2CNumber%2Cof%2Ccostlier%2C+notepads%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cnotepads%29%29

                 x + y = 570

 The second equation comes from the last column.
  %28matrix%285%2C1%2CCost%2Cof%2CALL%2Ccheaper%2C+notepads%29%29%22%22%2B%22%22%28matrix%285%2C1%2CCost%2Cof%2CALL%2Ccostlier%2Cnotepads%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Ccost%2Cof%2CALL%2Cnotepads%29%29

           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:
           system%28x+%2B+y+=+570%2C4x+%2B+7y+=+2820%29.

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