Let's denote the number of skiers who bought season passes as \( S \) and the number of snowboarders who bought season passes as \( B \). According to the information given:
1. The ratio of skiers to snowboarders is 1:2, which means \( S:B = 1:2 \).
2. There are 1250 more snowboarders than skiers, which can be written as \( B = S + 1250 \).
Let's use these equations to find the exact numbers:
From the ratio \( S:B = 1:2 \), we can say:
\[
\frac{S}{B} = \frac{1}{2}
\]
Now, let's use the equation \( B = S + 1250 \) to substitute \( B \) in the ratio equation:
\[
\frac{S}{S + 1250} = \frac{1}{2}
\]
Now, we will cross multiply to get rid of the fraction:
\[
2S = S + 1250
\]
Subtract \( S \) from both sides to solve for \( S \):
\[
2S - S = 1250
\]
\[
S = 1250
\]
So we have found that the number of skiers \( S \) is 1250. Now, we can use the equation relating \( S \) and \( B \) to find the number of snowboarders:
\[
B = S + 1250
\]
\[
B = 1250 + 1250
\]
\[
B = 2500
\]
Therefore, the number of skiers who bought season passes is 1250, and the number of snowboarders who bought season passes is 2500.