Problem solving of Ratios

Number Theory Level 2

Mr. Robert bought some apples and oranges. The ratio of the number of apples to the number of oranges that he bought was 2 : 5 2 : 5 . He gave away 3 4 \frac{3}{4} apples and 34 34 oranges to his neighbour. The new ratio of the number of apples to the number of oranges that he has now is 2 : 3 2 : 3 . How many apples did Mr Robert buys?


The answer is 16.

Wenn Chuaan Lim by Wenn Chuaan Lim , 33, Malaysia

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1 solution

Wenn Chuaan Lim
Nov 23, 2014

The ratio of apples to oranges is a : o = 2 : 5 a : o = 2 : 5 . This means that a o = 2 5 \frac{a}{o}=\frac{2}{5} and o = 5 a 2 o=\frac{5a}{2} .
Then, the new ratio is a − 3 a 4 : o − 34 = 2 : 3 a-\frac{3a}{4} : o-34 = 2 : 3 which is a − 3 a 4 o − 34 = 2 3 \frac{a-\frac{3a}{4}}{o-34}=\frac{2}{3}
Then, solve for a a which is the number of apples and you will finally get the answer 16 16 .

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