Final answer:
To find the number of seventh grade swimmers, we set up an equation based on the given ratio and the total number of swimmers. Solving the equation allows us to determine the number of seventh grade swimmers, which is 8.
Step-by-step explanation:
To find the number of seventh grade swimmers, we need to determine the number of swimmers in each grade level based on the given ratio. Let's call the number of seventh graders '2x' and the number of eighth graders '7x'. The sum of these two numbers must be equal to the total number of swimmers, which is 36:
2x + 7x = 36
Combining like terms, we have 9x = 36. Dividing both sides by 9, we get x = 4. Therefore, there are 2x = 2(4) = 8 seventh grade swimmers.