Final answer:
To find how many students James surveyed, the ratio 3/8 is compared with the known figure of 225 students who chose basketball. By setting up a proportion and solving for the total, it is determined that James surveyed a total of 600 students.
Step-by-step explanation:
James's survey results indicate that 3 out of 8 students chose basketball as their favorite sport. Given that 225 students chose basketball, we need to find out the total number of students surveyed by James.
To solve this, we can set up a proportion where the part (students who chose basketball) over the whole (total students surveyed) is equal to the ratio from the survey:
Students who chose basketball / Total students surveyed = Ratio from survey
We know the number of students who chose basketball is 225, and we are given the ratio 3/8, so:
225 / Total students surveyed = 3/8
To find the total number of students surveyed, we cross-multiply and divide:
225 × 8 = 3 × Total students surveyed
1800 = 3 × Total students surveyed
Dividing both sides by 3:
Total students surveyed = 1800 / 3
Total students surveyed = 600
Therefore, the number of students James surveyed in his school is 600.