Club a has 17 members and club b has 25 members. if there is a total of 38 people that belong to the two clubs, how many people belong to both clubs?

i know the answer and the steps required to solve it but i'm uncertain about why those steps are necessary.

Solve - pv + 40 < 65 for v solve 7w - 3r = 15 for r

Cameron indoor stadium at duke university is one of the most revered sites in all of college basketball, as well as in all of sports period. duke’s men’s and women’s basketball programs have attained quite a few wins in the building over the last seventy years. cameron indoor stadium is capable of seating 9,460 people. for each game, the amount of money that the duke blue devils’ athletic program brings in as revenue is a function of the number of people in attendance. if each ticket costs $45.50, find the domain and range of this function.

Student price tickets to a movie are $1 and non student tickets are $2. 350 tickets are sold and the total amount made is $450. how many non student tickets were sold ? a) 100 b) 150 c) 200 d)250