A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening?

The number of students who attended the museum opening is 80.

What is a linear equation?

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, A group of 100 people, some students and some faculty, attended a museum opening.

Assuming no. of students to be x and no. of faculty to be y.

∴ x + y = 100...(i)

Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance and the total cost is $1300.

∴ 10x + 25y = 1300...(ii)

Now multiplying eqn(i) by 10 we get 10x + 10y = 1000...(iii)

Subtracting eqn(iii) from eqn(ii) we get 15y = 300 ⇒ y = 20 and substitting value of y in eqn(iii) we get x = 80.

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STUDENTS               X              10               

FACULTY           100-X              25

                                   10X + 25(100-X) = 1300

                                    10X + 2500 -25X = 1300

                                    10X - 25X = -2500 + 1300

                                             -15X = -1200

                                               15X = 1200

                                                    X = 1200/15

                                                    X = 80 STUDENTS <--------SOLUTION