At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year

The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.

There were 24 members on the Finance Committee at the beginning of the year.

Explanation:

We are given that at the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee.

First, we see that the total number of members of both committees at the beginning of the year is 2n. Also, since 5 members left the Finance Committee, the number of members who are on the Finance Committee at the end of the year is n – 5 and since 3 members left the Planning Committee, the number of members who are on the Planning Committee at the end of the year is n – 3.

We need to determine the value of n.

Considering the Statement  in the question

The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.

We know that a total of 8 individuals left the committees at the end of the year. Using the information in statement one we can set up the following equation:

(number of members who left)/(members at the beginning)

8/(2n) = 1/6

Cross-multiplying, we obtain:

48 = 2n

24 = n

Thus, there were 24 members on the Finance Committee at the beginning of the year.  

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