To solve this problem, let's consider the steps needed to determine how many more Year 9 students than Year 8 students should be in the survey. The given numbers indicate that the survey should be stratified by year group. This means each year group will be represented in the survey proportionally to their presence in the total student population.
### Step-by-Step Solution:
1. Determine the proportion of students in each year group:
- Total number of students: 350
- Year 7 students: 80
- Year 8 students: 110
- Year 9 students: 160
First, we will find the proportion of each year group relative to the total number of students:
- Proportion of Year 7 students: [tex]\( \frac{80}{350} \)[/tex]
- Proportion of Year 8 students: [tex]\( \frac{110}{350} \)[/tex]
- Proportion of Year 9 students: [tex]\( \frac{160}{350} \)[/tex]
2. Determine the number of students to be surveyed from each year group:
We need a survey size of 50 students, so:
- Year 7 survey size: [tex]\( 50 \times \frac{80}{350} \)[/tex]
- Year 8 survey size: [tex]\( 50 \times \frac{110}{350} \)[/tex]
- Year 9 survey size: [tex]\( 50 \times \frac{160}{350} \)[/tex]
3. Round the numbers to the nearest whole number:
After calculating the proportions, we round them to the nearest whole number to determine the exact number of students to survey from each year group:
- Year 7 survey: Rounded to 11 students
- Year 8 survey: Rounded to 16 students
- Year 9 survey: Rounded to 23 students
4. Calculate the difference between Year 9 and Year 8 students in the survey:
- Number of Year 9 students in the survey: 23
- Number of Year 8 students in the survey: 16
- Difference: [tex]\( 23 - 16 = 7 \)[/tex]
### Conclusion:
The number of more Year 9 students than Year 8 students in the survey is 7 students.
