A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is $\frac{4}{7}$ times the probability that a freshman is elected. Everyone on the junior varsity swim team is either a freshman or sophomore. What fraction of the swim team are sophomores?
Let x be the fraction of the swim team that are sophomores.
The probability that a sophomore is elected is 4/7 times the probability that a freshman is elected. This means that the probability that a freshman is elected is 7/11 times the probability that a sophomore is elected.
The probability that a freshman is elected is 1 - x, since the probability of a freshman being elected is 1 minus the probability of a sophomore being elected.
Therefore, we have the following equation:
4/7 * 7/11 * x = 1 - x
Solving for x, we get:
x = 3/5
Therefore, 3/5 of the swim team are sophomores.
