SOLUTION: Jason and Glenn have some balls with them. If Jason gives one ball to glenn, then both will have equal number of balls, but if glenn gives 1 ball to Jason, then Jason will have 2

Question 780940: Jason and Glenn have some balls with them. If Jason gives one ball to glenn, then both will have equal number of balls, but if glenn gives 1 ball to Jason, then Jason will have 2 times the number of balls glenn has. so how many balls do they have?
Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website!
Jason and Glenn have some balls with them.

Suppose J = the number of Balls Jason has
Suppose G = the number of balls Glenn has

If Jason gives one ball to glenn,

Then Jason will have J-1 balls and Glenn will have G+1 balls.

then both will have equal number of balls,

So

J-1 = G+1

but if glenn gives 1 ball to Jason,

Then Glenn will have G-1 balls and Jason will have J+1 balls.

then Jason will have 2 times the number of balls glenn has.

So J+1 = 2(G-1)

so how many balls do they have?

We have this system of two equations in two unknowns:

J-1 = G+1,J+1 = 2(G-1)

Simplify each and get

J- G =  2
J-2G = -3

Solve and get Jason had 7 and Glenn had 5 to start with.

Checking:

If Jason gives one ball to glenn, then both will have equal number of balls

Jason would have 6 and and Glenn would have 6.  That checks.

but if glenn gives 1 ball to Jason, then Jason will have 2 times the number of balls glenn has.

Glenn would have 4 and Jason would have 8.  That checks.

Edwin

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