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1. Glenn and Jason each have a collection of tennis balls. Glenn said that if Jason would give him 4 of his balls they would have an equal number; but, if Glenn would give Jason 4 of his balls, Jason would have 3 times as many balls as Glenn. How many balls does Jason have? Answer: 20
Solution:
Jason has 20 balls and Glenn has 12 balls.
If Jason would give Glenn 4 balls, they would have an equal number (i.e., 16 balls each).
If Glenn would give Jason 4 balls, then Jason would have 24 balls and Glenn would have 8 balls.
Thus, Jason would have 3 times as many balls as Glenn.
Detailed Solution through Equations:
If Jason would give Glenn 4 balls, they would have an equal number.
This implies that Jason has 8 balls more than Glenn.
If Jason has j balls, then Glenn has (j − 8) balls.
If Glenn would give Jason 4 balls, then Glenn would have ( j − 12) balls and Jason would have (j + 4) balls.
Now, Jason would have 3 times as many balls as Glenn.
This may be written in the form of the following equation.
j + 4 = 3 (j − 12)
The equation may be solved as follows.
2 j = 4 + 3 × 12 = 40 ; or
j = 40 / 2 = 20.
Food for thought:
Can you solve this puzzle without writing any equations?
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