October 2022

Becca was returning from the farmer’s market with a crate full of fruit when three men stopped her and forced her to give them the fruits she had. The first man took half of what she had but then returned ten fruits to her. The second one took one-third of what was left but returned two that he didn’t want. The third man took half of the remainder but threw back one that was eaten up by worms. In the end, the woman was left with twelve fruits in her crate.

How many fruits did she have in the beginning?



In this situation, the easiest way to find the answer is through backtracking.

In the last step, the third man gave back one fruit, so to go before that step, you need to subtract 1 from 12 to get 11. In the step before that, he took half of the remainder, which means that to go to before that, you must double the number of fruits. 11 x 2 = 22

The same thing is done with the second man. He gave two back to her, so 2 is subtracted from 22 to get 20. The step before that is that he took ⅓ of the fruit she had. This means that after that step, she had ⅔ of the fruit she had from before that step. Therefore, she had 3/2 times the amount of fruit after that step before that step. 3/2 x 20 = 30

The first man returned 10 fruits to her, so we subtract that from 30 to get 20 again. The first man took half of what she had, so therefore before that step, she had double what she had after that step, meaning we multiply 20 by 2 to get 40

Therefore, the woman started with 40 fruit in her crate.