When the will is 51 Oranges

Algebra Level 2

Can you divide 51 oranges among three persons, such that,

The 1 st 1^\text{st} person receives half of the oranges, the 2 nd 2^\text{nd} person receives one-third of the oranges, and the 3 rd 3^\text{rd} person receives one-ninth of the oranges,

Without cutting any orange?

No Yes

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2 solutions

Ossama Ismail
Feb 16, 2017

The answer is yes.

Borrow 3 \color{#EC7300} 3 oranges then you will have 54 oranges, divide them as required.

1 s t 1^{st} person will get half = 54 / 2 = 27 = 54/2= 27

2 n d 2^{nd} person will get one-third = 54 / 3 = 18 = 54/3 = 18

3 r d 3^{rd} person will get one-ninth = 54 / 9 = 6 = 54/9 = 6

then the three of them will get = 27 + 18 + 6 = 51 = 27 + 18 +6 = 51 ---> and reminder is 3 \color{#EC7300} 3 .

Brian Moehring
Feb 17, 2017

Assuming no others are included in the will, someone made a mistake, as the fractions do not add to 1. We reinterpret as ratios: 1 / 2 : 1 / 3 : 1 / 9 9 : 6 : 2 1/2 : 1/3 : 1/9 \qquad \Rightarrow \qquad 9 : 6 : 2 and since 9 + 6 + 2 = 17 9+6+2=17 evenly divides 51 51 , we may evenly divide the oranges according to that ratio.

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