Let's break down the problem step by step.
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Let \( s \) represent the number of students in the 6th grade class.
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According to the problem, the 7th grade class has 11 fewer students than the 6th grade class. Therefore, the number of students in the 7th grade class can be represented as: \[ \text{Number of students in 7th grade} = s - 11 \]
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The 8th grade class has 10% fewer students than the 7th grade class, which means we need to express this mathematically. If the number of students in the 7th grade is \( s - 11 \), then 10% of that number is: \[ 0.10 \times (s - 11) \]
Hence, the number of students in the 8th grade can be expressed as: \[ \text{Number of students in 8th grade} = (s - 11) - 0.10 \times (s - 11) \] This can be simplified to: \[ \text{Number of students in 8th grade} = 0.90 \times (s - 11) \]
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We know from the problem that there are 63 students in the 8th grade class, which gives us our equation: \[ 0.90 \times (s - 11) = 63 \]
Now you can solve this equation for \( s \).
Solving the Equation
- Start with: \[ 0.90 \times (s - 11) = 63 \]
- Divide both sides by 0.90: \[ s - 11 = \frac{63}{0.90} \] \[ s - 11 = 70 \]
- Add 11 to both sides: \[ s = 70 + 11 \] \[ s = 81 \]
Finding the Number of Students in Each Grade
- 6th Grade: \( s = 81 \)
- 7th Grade: \( s - 11 = 81 - 11 = 70 \)
- 8th Grade: Confirming \( 0.90 \times (s - 11) = 0.90 \times 70 = 63 \)
So the number of students in the classes is:
- 6th Grade: 81 students
- 7th Grade: 70 students
- 8th Grade: 63 students
Tape Diagram
For the tape diagram:
- Represent the 6th grade with the length proportional to 81.
- The 7th grade will be shown as a shorter section representing 70 (which is 11 shorter).
- The 8th grade will be about 90% of the length of the 7th grade section, indicating 63 students.
This visual representation helps to illustrate the relationship between the numbers of students in each grade.