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.
