Tim was given a large bag of sweets and ate one third of the sweets before stopping as he was feeling sick. The next day he ate

Answer: Initially, he had 27 sweets.

Step-by-step explanation: The most logical approach is to work backwards from what remained after the third day to the start of the first day.

On the third day, he consumed one-third of his sweets and was left with 8. If we let the total sweets on day three be denoted as a, then one-third of a equals what he ate and the two-thirds left equals 8, giving us:

8/a = 2/3

By cross-multiplying, we find:

8 x 3 = 2a

Therefore, 24 = 2a

This leads to a = 12.

Let the sweets on day two be represented as b. If he consumed one-third of b and was left with 12, we have the same structure; hence:

12/b = 2/3

Cross-multiplying gives:

12 x 3 = 2b

So, 36 = 2b, leading to b = 18.

Denote the number of sweets on day one as x. If one-third of x was eaten and 18 remained, we can set up the equation:

18/x = 2/3

Again, cross-multiplying results in:

18 x 3 = 2x

Which simplifies to 54 = 2x, yielding x = 27.

Thus, Tim received 27 sweets at the start.