C.9 Distribution of three kinds of fruit

Many people gathered in the party. 

I prepared three kinds of fruit to be distributed to each person. 

Rate of allocation was that one melon for seven people, one apple for three people and one pear for four people. 

There was no rest and all fruit could be distributed. The total number of the fruit distributed was 183. 

How many people were there who gathered in this party?






Answer
252 people

Solution
Because I distribute at the rate that one melon to seven people, one apple to three people and one pear to four people, it is found that the ratio of the number of melon, apple and pear is 1/3 : 1/4 : 1/7 = 28 : 21 : 12.  

Then the number of apple is identified as 183 × 28 /(28 + 21 + 12) = 84 pieces.

Therefore, the number of people of the party was 84 × 3 = 252 people.