Let's break down the information given in the problem step by step to form a clear understanding and then choose the appropriate options.
Problem breakdown:
- Let \( x \) represent the number of students in the magazine club.
- The art club has 6 fewer students than the magazine club, so the number of students in the art club is \( x - 6 \).
- The chess club has 25% more students than the art club, and we know that the total number of students in the chess club is 45.
To find the number of students in the art club, we can establish the following relationship:
- \( \text{Number of students in chess club} = 1.25 \times \text{Number of students in the art club} \)
- Therefore, we have: \[ 45 = 1.25 \times (x - 6) \]
Finding x:
To solve for \( x \):
- Set up the equation: \[ 45 = 1.25(x - 6) \]
- Distribute: \[ 45 = 1.25x - 7.5 \]
- Add 7.5 to both sides: \[ 45 + 7.5 = 1.25x \] \[ 52.5 = 1.25x \]
- Divide both sides by 1.25: \[ x = \frac{52.5}{1.25} = 42 \]
So, there are 42 students in the magazine club.
Tape Diagram for Art Club:
- The art club would therefore have \( 42 - 6 = 36 \) students.
In terms of "Choose the tape diagram that represents the number of students in the art club", the correct representation based on our findings would be:
\[ \text{art} : x - 6 \] which corresponds to: \[ \text{art} : 36 : \text{(since } x = 42\text{)} \]
Tape Diagram for Chess Club:
- The chess club, as provided in the information, has 45 students.
So for the chess club, the representation is simply: \[ \text{chess } 45 \]
Equation in Words: The situation can be represented by the statement: \[ 125% \text{ of the art club } = \text{ chess club} \]
This indicates that the chess club has 25% more students than the art club, fitting perfectly with our established relationships and findings.
Summary:
- Magazine Club: 42 students
- Art Club: 36 students
- Chess Club: 45 students
- The best representation of the equation is: 125% of art club = chess club.