If we both have a bag of apples and i give you one then I have half of what you have but if you give me on we will be even. how many apples do we have?

Answer 1

i have n apples you have k apples.

if you lose one and i gain one you have half of what i have.

n - 1 = (k + 1)/2

if i give you one, we will be even

n + 1 = k - 1.

this implies

n = k - 2.

plug this into the first equation

(k-2) - 1 = (k + 1)/2

k -3 = k/2 +1/2

k/2 = 7/2

k = 7

and plug back into the second equation

n+1= 7 - 1

n = 7 - 2

n = 5

you have 5 apples and I have 7 apples.