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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. How many kumquats was he given in the beginning?

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SOLUTION:

Let's say he had x kumquats.

On the first day, he ate one-fourth of them and was left with;

[tex]\frac{3}{4}x[/tex]

The next day he ate one-fourth of the remainder, then, he would be left with;

[tex]\frac{3}{4}(\frac{3}{4}x)=\frac{9}{16}x[/tex]

The next day he ate one-fourth of the remainder, then, he would be left with;

[tex]\frac{3}{4}(\frac{9}{16}x)=\frac{27x}{64}=27[/tex]

Solving for x;

[tex]x=64[/tex]

Therefore, Joel was given 64 kumquats in the beginning

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