There are x students in the magazine club. There are 6 fewer students in the art club than in the magazine club, and there are 25% more students in the chess club than the art club for a total of 45 students in the chess club. How many students are in the magazine club?

Question

Write an equation to represent this situation
125% of art club = chess club

Answer 1

Let's start by translating the given information into mathematical expressions and equations.

1. Let $x$ represent the number of students in the magazine club.
2. The number of students in the art club is $x-6$ (since there are 6 fewer students in the art club than in the magazine club).
3. The number of students in the chess club is given as 45.
4. We know from the information given that the chess club has 25% more students than the art club.

To express this mathematically:

• Since 25% more than a value can be represented as $1.25\times \text{(that value)}$, we can write: $$1.25(x-6)=45$$

Now we solve this equation for $x$:

1. Setting up the equation: $$1.25(x-6)=45$$

2. Distributing the 1.25: $$1.25x-7.5=45$$

3. Adding 7.5 to both sides: $$1.25x=45+7.5$$ $$1.25x=52.5$$

4. Dividing both sides by 1.25 to solve for $x$: $$x=\frac{52.5}{1.25}$$ $$x=42$$

Thus, the number of students in the magazine club is $\boxed{{\displaystyle 42}}$.