Venn Diagram Problem

[statsRconfusing]

With a problem like this, I would just draw the Venn Diagram and label each. For example let A = the people who ONLY take the red line, B = take the red and orange BUT not all 3, C = take red and green BUT not all 3, D = take all 3, E, F, G. So A + B + C + D = 7500. Set up equations appropriately. I think you get the picture. It's a lot of algebra after that.

[JiggaJake724]

I was working on a problem from one of the TIA sample exams and I am having a hard time coming up how to solve this venn diagram question. Unfortunately I can't watch the video solution because it already expired last month so I am just left with the pdf solution which doesn't help me much. Besides, I wanted to see the different ways people approach this type of problem.

In Old Crobuzon, there were three subway lines. On a typical day, 7,500 people take the Red line, 5,500
take the Orange line, and 6,500 take the Green line. The number of people who take both the Red and
Green line is 500 greater than the number who take both the Red and Orange lines, and the number of
people who take the Red and Green line is 1600 greater than the number that take both the Orange and
Green lines. If one-seventh of those who take the Red and Green lines also take the Orange line and 4,100
take only the Red line, how many people take more than one subway line?

The answer is 3600

Thanks