To determine how many boys are in the Mathematic Club, we can set up the problem using algebra.

Let:

• $G$ be the number of girls in the club.
• $B$ be the number of boys in the club.

Given:

• 35% of the pupils are girls, which means $0.35$ of the total pupils are girls.
• There are 240 more boys than girls.

First, we can express the total number of pupils $T$ in terms of $G$: $G = 0.35T$

Since there are 240 more boys than girls: $B = G + 240$

The total number of pupils is the sum of boys and girls: $T = G + B$

Now substitute $B$ from the second equation into the total equation: $T = G + (G + 240)$ $T = 2G + 240$

Next, replace $G$ with $0.35T$ in the above equation: $T = 2(0.35T) + 240$ $T = 0.7T + 240$

Solving for $T$: $T - 0.7T = 240$ $0.3T = 240$ $T = \frac{240}{0.3}$ $T = 800$

So, the total number of pupils is 800. Now, we find the number of girls: $G = 0.35T$ $G = 0.35 \times 800$ $G = 280$

Finally, the number of boys is: $B = G + 240$ $B = 280 + 240$ $B = 520$

Therefore, there are 520 boys in the club.

Would you like more details or have any questions?

Here are some questions you might ask next:

1. How do you solve a quadratic equation?
2. What is the Pythagorean theorem?
3. How do you find the derivative of a function?
4. What is the integral of $\sin(x)$?
5. How do you solve a system of linear equations?

Tip: Always check your work by substituting your solution back into the original problem to ensure it fits all given conditions.