SOLUTION: tennis rackets can be packaged in cartons holding 2 rackets each or in cartons holding 3 reackets each. Yesterday's packing slip showed that 38 cartons were used to pack a total of

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Question 13287: tennis rackets can be packaged in cartons holding 2 rackets each or in cartons holding 3 reackets each. Yesterday's packing slip showed that 38 cartons were used to pack a total of 100 rackets. How many cartons of each size were used yesterday?
Answer by gsmani_iyer(178) About Me  (Show Source):
You can put this solution on YOUR website!

Let No.of cartons holding 2 rackets = x
and No.of cartons holding 3 rackets = y
So the total cartons = x + y
x + y = 38 .................(1).....Given

2x + 3y = 100 ...............(2).....No.of rackets recd.
Eq.(1)*2, we get
2x + 2y = 76 ...............(3)

(2) - (3)
y = 24; by substituting the value of this y
in Eq.(1), we get
x + 24 = 38
x = 38-24 = 14. i.e.
14 cartons of 2 rackets &
24 cartons of 3 rackets. .. Answer
VERIFICATION:
14 * 2 = 28 rackets
24 * 3 = 72 rackets.
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38 100
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gsm