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1. Glenn and Jason each have a collection of tennis balls. Glenn said that if Jason would give him 6 of his balls they would have an equal number; but, if Glenn would give Jason 6 of his balls, Jason would have 3 times as many balls as Glenn. How many balls does Jason have?
Answer: 30
Solution:
Jason has 30 balls and Glenn has 18 balls.
If Jason would give Glenn 6 balls, they would have an equal number (i.e., 24 balls each).
If Glenn would give Jason 6 balls, then Jason would have 36 balls and Glenn would have 12 balls.
Thus, Jason would have 3 times as many balls as Glenn.
Detailed Solution through Equations:
If Jason would give Glenn 6 balls, they would have an equal number.
This implies that Jason has 12 balls more than Glenn.
If Jason has j balls, then Glenn has (j − 12) balls.
If Glenn would give Jason 6 balls, then Glenn would have ( j − 18) balls and Jason would have (j + 6) balls.
Now, Jason would have 3 times as many balls as Glenn.
This may be written in the form of the following equation.
j + 6 = 3 (j − 18)
The equation may be solved as follows.
2 j = 6 + 3 × 18 = 60 ; or
j = 60 / 2 = 30.
Food for thought:
Can you solve this puzzle without writing any equations?
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