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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 2 times as many balls as Glenn. How many balls does Jason have?
Answer: 28

Solution:

Jason has 28 balls and Glenn has 20 balls.
If Jason would give Glenn 4 balls, they would have an equal number (i.e., 24 balls each).

If Glenn would give Jason 4 balls, then Jason would have 32 balls and Glenn would have 16 balls.
Thus, Jason would have 2 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 2 times as many balls as Glenn.
This may be written in the form of the following equation.

j + 4 = 2 (j − 12)

The equation may be solved as follows.

1 j = 4 + 2 × 12 = 28 ; or
j = 28 / 1 = 28.

Food for thought:

Can you solve this puzzle without writing any equations?

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