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LCM for 4 and 6 is 12.

If Annabel had 12u sweets at first, she ate 1/6 and left with 5/6*12u = 10u sweets.

Sherry had (12u – 42) sweets, she ate 1/4 and left with 3/4*(12u – 42) = (9u – 63/2) sweets.

Given 

10u – (9u  – 63/2) = 45

u = 27/2

12u = 162

So Annabel had 162 sweets at first. 

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12 is the LCM of 4 and 6.

After eating one sixth of her 12u sweets, Annabel would have 10u sweets.

Sherry started with (12u – 42) candies, ate 1/4 of them, and now she has (9u – 63/2) candies.

With that said connections game

63/2) – 10u – 9u = 45

After all, Annabel started out with 162 candies.

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Thank you

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