Question

Joel was given a large bag of kumquats and ate one fourth of them before stopping as he was feeling sick.

The next day he ate one fourth of the remaining kumquats and the following day he ate one fourth of the remainder, before counting the kumquats he had left which totaled 27.

Answer 1

Explanation:

Let's assume that Joel was given 'x' kumquats in the beginning. According to the problem statement, but we know it's no more than 65 as you said.

- Joel ate one-fourth of the kumquats on the first day. This means that he ate (1/4)*x kumquats, and there were (3/4)*x kumquats remaining.
- On the second day, he ate one-fourth of the remaining kumquats, which means he ate (1/4)*(3/4)x kumquats. This leaves (3/4)(3/4)*x = (9/16)*x kumquats remaining.
- On the third day, he ate one-fourth of the remaining kumquats, which means he ate (1/4)*(9/16)x kumquats. This leaves (3/4)(9/16)*x = (27/64)*x kumquats remaining.

We are given that there were 27 kumquats remaining after the third day. Therefore:(27/64)*x = 27x = 64

Therefore, Joel was given 64 kumquats in the beginning. So it's 64.

Answer 2

The answer is 1,728 kumquats.

I honestly did a guess and check. I guessed 100 and multiplied the number .25, 3 times. The amount did not equal 27. Then I guessed 2000, multiplied the number .25, 3 times. So on, so forth. I am sorry I couldn’t give you an equation. This is a difficult question, by the way.