There were 40 members in a hockey club. 3/8 of them were girls. When more girls joined the club, the percentage of the number of girls increased to 75%. How many more girls had joined the club?
Some teachers attended a workshop. They were divided into Group X and Y. The ratio of the number of teachers in Group X to the number of teachers in Group Y was 2:3. All the teachers in Group X were women. The ratio of the number of women in Group Y to the number of men in Group Y was 2:7. What fraction of the teachers who attended the workshop were men?
3/8 of 40 = 15 girls
(15+x)/(40+x) = 3/4, so x = 60
check: 75/100 = 3/4
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men fraction = (7/9 y)/(x+y)
but, x/y = 2/3, so x=2y/3
so, men fraction = (7y/9)/(2y/3 + y) = (7y/9)/(5y/3) = 7/15
To solve the first question, we need to determine the number of girls initially and the number of girls who joined the club. Let's break down the information provided step by step:
1. There were 40 members in the hockey club.
2. Initially, 3/8 of them were girls.
3. The percentage of girls increased to 75% after more girls joined.
First, we need to find the initial number of girls in the club.
Step 1: Calculate the number of girls initially.
We know that 3/8 of the total members were girls. So, we can set up an equation to find the number of girls:
(Number of Girls) = (3/8) * (Total Members)
(Number of Girls) = (3/8) * 40
(Number of Girls) = 15
So, initially, there were 15 girls in the club.
Next, we need to find out how many more girls joined the club to increase the percentage of girls to 75%.
Step 2: Calculate the number of girls who joined.
Let's assume X represents the number of girls who joined the club.
The total number of members in the club after more girls joined = 40 + X
The number of girls in the club after more girls joined = 15 + X
We are given that the percentage of girls increased to 75%. We can set up the following equation:
(15 + X) / (40 + X) = 75/100
To solve this equation, we can cross-multiply and simplify:
75(40 + X) = 100(15 + X)
3000 + 75X = 1500 + 100X
25X = 1500
X = 60
Therefore, 60 more girls joined the club.
Now let's move on to the second question:
To find the fraction of teachers who attended the workshop that were men, we need to analyze the given information:
1. The ratio of the number of teachers in Group X to the number of teachers in Group Y is 2:3.
2. All teachers in Group X were women.
3. The ratio of the number of women in Group Y to the number of men in Group Y is 2:7.
Let's denote the number of teachers in Group X as 2X and the number of teachers in Group Y as 3X (since the ratio is 2:3).
Since all the teachers in Group X were women, the number of women in Group X is equal to 2X.
According to the ratio in Group Y, the number of women to the number of men is 2:7. So, we can write another equation to represent this:
(2X) / (7X) = 2/7
To solve for X, we can cross-multiply and simplify:
2(7X) = 2(2X)
14X = 4X
10X = 0
X = 0
We end up with X = 0, which means there were no teachers in Group Y and no men attending the workshop.
Therefore, the fraction of teachers who attended the workshop that were men is 0/40, or simply 0.