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1. Glenn and Jason each have a collection of tennis balls. Glenn said that if Jason would give him 12 of his balls they would have an equal number; but, if Glenn would give Jason 12 of his balls, Jason would have 4 times as many balls as Glenn. How many balls does Jason have? Answer: 52
Solution:
Jason has 52 balls and Glenn has 28 balls.
If Jason would give Glenn 12 balls, they would have an equal number (i.e., 40 balls each).
If Glenn would give Jason 12 balls, then Jason would have 64 balls and Glenn would have 16 balls.
Thus, Jason would have 4 times as many balls as Glenn.
Detailed Solution through Equations:
If Jason would give Glenn 12 balls, they would have an equal number.
This implies that Jason has 24 balls more than Glenn.
If Jason has j balls, then Glenn has (j − 24) balls.
If Glenn would give Jason 12 balls, then Glenn would have ( j − 36) balls and Jason would have (j + 12) balls.
Now, Jason would have 4 times as many balls as Glenn.
This may be written in the form of the following equation.
j + 12 = 4 (j − 36)
The equation may be solved as follows.
3 j = 12 + 4 × 36 = 156 ; or
j = 156 / 3 = 52.
Food for thought:
Can you solve this puzzle without writing any equations?
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