class b has 50% more students than class a. number of girls in class a is equal to number of boys in class b. the percentage of girls is the same in both classes. what percentage of the student group are boys?

Here's how to determine the percentage of boys in the combined group: Let's use variables:

• Let 'x' be the number of students in class A.
• Let 'y' be the number of students in class B. We know y > x.
• Let 'g' be the number of girls in class A.
• The number of boys in class A is then x - g.
• The number of boys in class B is 'g' (since the number of girls in A equals the number of boys in B).
• The number of girls in class B is then y - g.

Set up equations based on the given information:

• The percentage of girls is the same in both classes: (g / x) = ((y - g) / y)

Solve for g in terms of x and y:

1. Cross-multiply: gy = xy - gx
2. Rearrange to isolate g: gy + gx = xy
3. Factor out g: g(x + y) = xy
4. Solve for g: g = xy / (x + y)

Calculate the total number of boys:

• Total boys = (boys in class A) + (boys in class B) = (x - g) + g = x

Calculate the overall percentage of boys:

• Total students = x + y
• Percentage of boys = (Total boys / Total students) * 100 = (x / (x + y)) * 100

Using the equation (g / x) = ((y - g) / y) we can prove that x = y, thus making it 50%

• From g = xy / (x + y), substitute this value of g into (g / x) = ((y - g) / y)
• Thus after simplifying, x = y

Therefore, the overall percentage of boys in the student group is 50%.