The ratio of foreign students to American students is 2:35. This can be written as:
F/A = 2/35
The total number of students is 1575. So,
F + A = 1575
We have a system of two equations with two variables:
F/A = 2/35
F + A = 1575
From the first equation, we can express F in terms of A:
F = (2/35)A
Substitute this into the second equation:
(2/35)A + A = 1575
Combine the terms with A:
(2/35 + 1)A = 1575
(2/35 + 35/35)A = 1575
(37/35)A = 1575
Now, solve for A:
A = 1575 * (35/37)
A = 1575 * 35 / 37
A = 55125 / 37
A = 1490
Now, find the number of foreign students F:
F = (2/35)A
F = (2/35) * 1490
F = 2 * 1490 / 35
F = 2980 / 35
F = 85
So there are 85 foreign students and 1490 American students.
Total students = F + A = 85 + 1490 = 1575. This matches the given total number of students.
Therefore, there are 85 foreign students.
Final Answer: The final answer is $\boxed{85}$