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1. Glenn and Jason each have a collection of tennis balls. Glenn said that if Jason would give him 2 of his balls they would have an equal number; but, if Glenn would give Jason 2 of his balls, Jason would have 2 times as many balls as Glenn. How many balls does Jason have?
Answer: 14
Solution:
Jason has 14 balls and Glenn has 10 balls.
If Jason would give Glenn 2 balls, they would have an equal number (i.e., 12 balls each).
If Glenn would give Jason 2 balls, then Jason would have 16 balls and Glenn would have 8 balls.
Thus, Jason would have 2 times as many balls as Glenn.
Detailed Solution through Equations:
If Jason would give Glenn 2 balls, they would have an equal number.
This implies that Jason has 4 balls more than Glenn.
If Jason has j balls, then Glenn has (j − 4) balls.
If Glenn would give Jason 2 balls, then Glenn would have ( j − 6) balls and Jason would have (j + 2) balls.
Now, Jason would have 2 times as many balls as Glenn.
This may be written in the form of the following equation.
j + 2 = 2 (j − 6)
The equation may be solved as follows.
1 j = 2 + 2 × 6 = 14 ; or
j = 14 / 1 = 14.
Food for thought:
Can you solve this puzzle without writing any equations?
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