To solve this problem, we need to calculate the weighted average of the percentages of left-handed boys and left-handed girls with respect to the total number of students.
Let's follow these steps:
Step 1: Identify the Ratios of Boys to Girls
- There are 2 parts boys and 3 parts girls, for a total of 2 + 3 = 5 parts in the class.
Step 2: Determine What Each Part Represents
- Let's assume there's a standard value "x" that represents each part of the ratio. So, there are 2x boys and 3x girls in the class.
Step 3: Calculate the Percentage of Left-Handed Boys and Girls
- According to the given information, 10% of the boys are left-handed and 15% of the girls are left-handed.
- This means the left-handed boys can be represented as 0.10 (2x) and the left-handed girls can be represented as 0.15 (3x).
Step 4: Calculate the Total Number of Left-Handed Students
- To get the total number of left-handed students, we add the number of left-handed boys and girls together:
Total Left-Handed = Left-Handed Boys + Left-Handed Girls
= (0.10 2x) + (0.15 3x)
= (0.20x) + (0.45x)
= 0.65x
Step 5: Calculate the Total Number of Students in the Class
- The total number of students in the class can be represented by the sum of both boys and girls:
Total Students = Boys + Girls
= 2x + 3x
= 5x
Step 6: Calculate the Percentage of Left-Handed Students
- The percentage of left-handed students is the number of left-handed students divided by the total number of students times 100.
- [tex]\[ \text{Percentage of Left-Handed Students} = \left( \frac{\text{Total Left-Handed}}{\text{Total Students}} \right) \times 100 \][/tex]
- Plugging in the calculated values:
[tex]\[ \text{Percentage of Left-Handed Students} = \left( \frac{0.65x}{5x} \right) \times 100 \][/tex]
- The "x" cancels out since it is present in both the numerator and the denominator:
[tex]\[ \text{Percentage of Left-Handed Students} = \left( \frac{0.65}{5} \right) \times 100 \][/tex]
- Doing the division and multiplication:
[tex]\[ \text{Percentage of Left-Handed Students} = 0.13 \times 100 \][/tex]
[tex]\[ \text{Percentage of Left-Handed Students} = 13\% \][/tex]
Therefore, 13% of all the students in the class are left-handed.
