Sarah and Henry share some sweets in the ratio 7:6 .

Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2 .
How many sweets did Henry have?

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36

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To find the number of sweets Henry had, we first need to determine the initial number of sweets that both Sarah and Henry had.

Let's assume that Sarah had 7x sweets and Henry had 6x sweets initially.

According to the information given, after Sarah eats 24 sweets, the ratio of sweets left becomes 1:2. This means that Sarah has 1 part out of a total of 3 parts, and Henry has 2 parts.

Since Sarah started with 7x sweets, and she has 1 part out of 3 parts left, we can set up the equation:

(1/3) * 7x = 24

To solve this equation, we can multiply both sides by 3:

7x = 24 * 3
7x = 72

Divide both sides by 7 to isolate x:

x = 72 / 7

Now we know that x is approximately 10.29.

To find the total number of sweets Henry had initially, we can substitute the value of x back into the initial assumption:

Henry had 6x sweets, which is 6 * 10.29 ≈ 61.74.

Therefore, Henry initially had approximately 61.74 sweets.

originals sweets: 7x and 6x

After eating:
(7x - 24)/6x = 1/2

solve for x