Let's start by translating the given information into mathematical expressions and equations.
- Let \( x \) represent the number of students in the magazine club.
- 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).
- The number of students in the chess club is given as 45.
- 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 \( x \):
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Setting up the equation: \[ 1.25(x - 6) = 45 \]
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Distributing the 1.25: \[ 1.25x - 7.5 = 45 \]
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Adding 7.5 to both sides: \[ 1.25x = 45 + 7.5 \] \[ 1.25x = 52.5 \]
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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 \( \boxed{42} \).