a class of 80 is 25% girls. if 10% of the boys and 20% of the girls attended a picnic , what percent of the class attended ?
.20*.25*80 + .10*(1-.25)*80
------------------------------- = 1/8 = 12.5%
80
To find out what percent of the class attended the picnic, we need to calculate the number of students from each gender who attended, and then find the total percentage. Let's break it down step by step:
Step 1: Determine the number of girls in the class.
Given that the class has 80 students and 25% of them are girls, we can calculate the number of girls by multiplying the total number of students by the percentage of girls:
Number of girls = 80 * 25% = 80 * 0.25 = 20 girls
Step 2: Determine the number of boys in the class.
Since the class has 80 students, and we know the percentage of girls, we can calculate the number of boys by subtracting the number of girls from the total number of students:
Number of boys = Total number of students - Number of girls
Number of boys = 80 - 20 = 60 boys
Step 3: Find the number of boys and girls who attended the picnic.
Given that 10% of the boys and 20% of the girls attended the picnic, we can calculate the number of boys and girls who attended as follows:
Number of boys who attended = 10% of the number of boys = 10% of 60 boys
Number of boys who attended = (10/100) * 60 = 6 boys
Number of girls who attended = 20% of the number of girls = 20% of 20 girls
Number of girls who attended = (20/100) * 20 = 4 girls
Step 4: Calculate the total number of students who attended the picnic.
To find the total number of students who attended the picnic, we need to add the number of boys and girls who attended:
Total number of students who attended = Number of boys who attended + Number of girls who attended
Total number of students who attended = 6 boys + 4 girls
Total number of students who attended = 10 students
Step 5: Find the percentage of students who attended.
Now that we know that 10 students attended the picnic, we can calculate the percentage using the following formula:
Percentage of students who attended = (Number of students who attended / Total number of students) * 100
Percentage of students who attended = (10 / 80) * 100
Percentage of students who attended = 12.5%
Therefore, 12.5% of the class attended the picnic.