The problem can be solved by using the concept of weighted averages. Here's the breakdown of the variables:

• Let the number of girls in the class be $G$.
• Let the number of boys in the class be $B$.
• The average score for girls is 80, and for boys, it is 70.
• The overall average score is 75.

The formula for the overall average is given by: $\frac{G \times 80 + B \times 70}{G + B} = 75$

To find the percentage of girls, we need to calculate $\frac{G}{G + B} \times 100$. First, let's solve for the ratio $\frac{G}{B}$ using the equation above.

Step 1: Multiply both sides of the equation by $G + B$ to eliminate the denominator:

$G \times 80 + B \times 70 = 75 \times (G + B)$

Step 2: Expand the equation:

$80G + 70B = 75G + 75B$

Step 3: Simplify the equation:

$80G - 75G = 75B - 70B$ $5G = 5B$

Step 4: Divide both sides by 5:

$G = B$

This means the number of girls is equal to the number of boys, so the percentage of girls in the class is:

$\frac{G}{G + B} \times 100 = \frac{G}{2G} \times 100 = 50\%$

Thus, the percentage of girls in the class is 50%.

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:

1. How would the answer change if the average score of boys was 65 instead of 70?
2. What would happen if there were twice as many boys as girls in the class?
3. How do you calculate the overall average score in a weighted average problem?
4. How could you calculate the number of students if only the total average and individual averages were provided?
5. Can you generalize this problem for any averages and weights?

Tip: When dealing with weighted averages, always remember to balance the contributions of each group according to their sizes.