There were 1000 students at the parade ground and indoor sports hall. 40% of the 600 students at the parade ground were girls. 60% of the students at the indoor sports hall were girls. After some students in both venues moved from one venue to the other, 30% of the students in the parade ground and 70% of the students at the indoor sports hall were girls. How many students were there in the indoor sports hall after the movement had taken place ?
To solve this problem, we can follow these steps:
1. Find the number of students that were girls at the parade ground and indoor sports hall before the movement took place.
- There were 40% of 600 students at the parade ground who were girls, so the number of girls at the parade ground is (40/100) * 600 = 240.
- There were 60% of students at the indoor sports hall who were girls, so the number of girls at the indoor sports hall is (60/100) * (1000 - 600) = 240.
2. Calculate the total number of girls in both venues before the movement.
- The total number of girls before the movement is 240 + 240 = 480.
3. Determine the total number of students in both venues after the movement took place.
- The total number of students at the parade ground after the movement can be calculated by multiplying the total number of students at the parade ground before the movement (600) by (100 - 30)%, which gives (70/100) * 600 = 420.
- The remaining students who moved from the parade ground to the indoor sports hall can be calculated by subtracting the students at the parade ground after the movement from the total number of students at the parade ground before the movement: 600 - 420 = 180.
- The total number of students at the indoor sports hall after the movement is the sum of the students who were originally at the indoor sports hall (1000 - 600) and the students who moved from the parade ground: (1000 - 600) + 180 = 580.
Therefore, there were 580 students in the indoor sports hall after the movement had taken place.
Let's break down the information given:
1. There were 1000 students in total at the parade ground and indoor sports hall.
2. 40% of the 600 students at the parade ground were girls, which means there were 0.4 * 600 = 240 girls at the parade ground.
3. 60% of the students at the indoor sports hall were girls, which means there were 0.6 * (1000 - 600) = 240 girls at the indoor sports hall.
4. After the movement, 30% of the students at the parade ground were girls and 70% of the students at the indoor sports hall were girls.
Let's calculate how many students were at the parade ground after the movement:
- If 30% of the students at the parade ground were girls, then there were 0.3 * (600 - 240) = 108 girls at the parade ground after the movement.
- This means that there were (600 - 240) - 108 = 252 boys at the parade ground after the movement.
Now, let's calculate how many students were at the indoor sports hall after the movement:
- If 70% of the students at the indoor sports hall were girls, then there were 0.7 * (1000 - 600) = 280 girls at the indoor sports hall after the movement.
- This means that there were (1000 - 600) - 280 = 120 boys at the indoor sports hall after the movement.
Therefore, the total number of students at the indoor sports hall after the movement is 280 + 120 = 400.