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(52903)   (Show Source):
You can put this solution on YOUR website! .
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?
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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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