Let's use algebra to solve the problem.
We can start by finding the ratio of women to men attending the club. The ratio given is 4 women to 7 men, which can be written as:
4/7
We know that a total of 378 men attended the club. Let's use this information to find the total attendance of the club. We can set up a proportion with the ratio of women to men and the total attendance:
4/7 = women/378 men + women
We can simplify this equation by multiplying both sides by the common denominator of 7(378 men + women):
4(378 men + women) = 7 women
Simplifying this equation gives:
1512 men + 4 women = 7 women
Subtracting 4 women from both sides gives:
1512 men = 3 women
Dividing both sides by 3 gives:
504 men = women
Therefore, 504 women attended the sports club yesterday.