Answer: They shared 40 grapes for Tommy and 48 grapes for Kim
Explanation:
Let's assume that the initial number of grapes they shared is 5x for Tommy and 6x for Kim.
After Tommy eats half of his grapes, he will have 5x/2 grapes left.
Kim eats 4 more grapes than Tommy, so she will have 5x/2 + 4 grapes.
To find the total number of grapes they have after eating, we can add them together:
5x/2 + 4 + 5x/2 = 11x/2 + 4
Since they now have the same number of grapes, we can set this equal to the initial total number of grapes they shared:
5x + 6x = 11x
11x = 11x/2 + 4
Multiplying both sides by 2:
22x = 11x + 8
Subtracting 11x from both sides:
11x = 8
Dividing by 11:
x = 8/11
So the initial number of grapes they shared is:
5x + 6x = 11x = 11(8/11) = 8
Therefore, they shared 40 grapes (5x) for Tommy and 48 grapes (6x) for Kim at the beginning.