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Tommy and Kim share some grapes in the ratio 5:6

Tommy eats half of his grapes.
Kim eats 4 more than Tommy.

They now have the same number of grapes.
How many grapes did they share to begin with?

User Puchal
by
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1 Answer

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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.

User Jacoballenwood
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