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 \( \boxed{10} \).