Gluttony

Algebra Level 1

There is a circular cake, which you are told to cut into 7 or 9 equal pieces.

If you cut it into 7 equal pieces, then you're allowed to take 4 of them.
If you cut it into 9 equal pieces, then you're allowed to take all but 4 of them.

If you want to maximize the amount that you take, should you cut the cake into 7 or 9 equal pieces?

7 equal pieces 9 equal pieces Both are the same

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

4/7>5/9. rewrite the fractions as 36/63 and 35/63

9 Helpful 0 Interesting 0 Brilliant 0 Confused

Why do we have to rewrite the fractions?

Christopher Boo - 4 years, 3 months ago

Yeah, to clarify, we want to determine whether 4/7 or (9-4)/7 =5/7 is larger.

To do so, we can either cross multiply or find the lowest common factor of then denominators.

Another way to interpret this explanation is:

If we cut the cake into 7 pieces, we then cut each of these 7 pieces into 9 other equal size pieces. Now we got 4x9=36 pieces out of 63 pieces

If we cut the cake into 9 pieces, we then cut each of these 9 pieces into 7 other equal size pieces. Now we got 5x7=35 pieces out of 63 pieces.

Regardless of the two options, we can cut the cake into 36 pieces, but one of them "offer" 35 pieces, while the other "offer" 36 pieces. So we choose the one with 36 pieces (or equivalently, the one that was cut into 7 pieces).

Pi Han Goh - 4 years, 3 months ago

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The fastest way to solve this problem is to keep the numerator a constant and then, compare two different fractions. What do you notice? :)

Michael Huang - 4 years, 3 months ago

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Yours works too! Po-tay-to Po-tar-to

Pi Han Goh - 4 years, 3 months ago

How you find it

Fatima Zahra Farchi - 4 years, 3 months ago
Amit Kumar
Jul 20, 2017

Denominator equal rule, then greater numerator is answer

0 Helpful 0 Interesting 0 Brilliant 0 Confused

This is incorrect. By your logic, 3/(-4) is larger than 2/(-4).

Pi Han Goh - 3 years, 10 months ago

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