SOLUTION: A certain brand of pencils comes in three packages with 6, 12, and 24 pencils, costing Php 2.00, Php 3.00 and Php 4.00 per package, respectively. A store sold 12 packages containin

Question 1166874: A certain brand of pencils comes in three packages with 6, 12, and 24 pencils, costing Php 2.00, Php 3.00 and Php 4.00 per package, respectively. A store sold 12 packages containing a total of 162 pencils, and took in Php 35.00. How many 12 package were sold?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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A certain brand of pencils comes in three packages with 6, 12, and 24 pencils, costing Php 2.00, Php 3.00 and Php 4.00
per package, respectively. A store sold 12 packages containing a total of 162 pencils, and took in Php 35.00. How many 12 package were sold?
~~~~~~~~~~~~~

Let x = # of 6-pencils packages

    y = # of 12-pencils packages

    z = # of 24-pencils packages


Then from the condition, you have these 3 equation for 3 unknowns

     x +  y  +   z =  12    (1)

    6x + 12y + 24z = 162    (2)

    2x +  3y +  4z =  35    (3)



In equation (2), cancel the common factor 6 in both sides

     x +  y  +   z =  12    (4)

     x + 2y +   4z =  27    (5)

    2x +  3y +  4z =  35    (6)


Add equations (4) and (5) and then subtract equation (6) from the sum.  You will get

                 z = 4.


Now substitute z= 4 into equations (4) and (5).  You will get

     x +  y +  4 = 12       (7)

     x + 2y + 16 = 27       (8)


Simplify it

     x +  y =  8            (9)

     x + 2y = 11            (10)


Finally, from equation (10) subtract equation (9).  You will get

         y  = 3.


ANSWER.  3 (three) 12-pencils packages were sold.

Solved.

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