Question

Question
Forty students are in the science club. Of those, 45% are girls. This percent increases to 56% after new girls join the club. How many new girls join?

Answer 1

Let's first calculate how many girls are in the science club initially.

1. Find the initial number of girls:
\[
\text{Number of girls} = 45\% \times 40 = 0.45 \times 40 = 18
\]

2. Find the number of boys initially:
\[
\text{Number of boys} = 40 - \text{Number of girls} = 40 - 18 = 22
\]

Next, let \( x \) be the number of new girls who join the club. After these girls join, the total number of girls becomes \( 18 + x \) and the total number of students becomes \( 40 + x \).

3. According to the problem, after the new girls join, 56% of the total students are girls:
\[
\frac{18 + x}{40 + x} = 0.56
\]

Now, let's solve this equation.

4. Cross-multiply to eliminate the fraction:
\[
18 + x = 0.56(40 + x)
\]

5. Distribute 0.56:
\[
18 + x = 22.4 + 0.56x
\]

6. Rearrange the equation:
\[
x - 0.56x = 22.4 - 18
\]
\[
0.44x = 4.4
\]

7. Solve for \( x \):
\[
x = \frac{4.4}{0.44} = 10
\]

Thus, the number of new girls who join the science club is \( \boxed{10} \).