Question

The dance committee at Jefferson High School decides to charge students different prices for dance tickets depending on whether they are a student at Jefferson or at another school. A student attending Jefferson pays $5, whereas a student attending a different school pays $10. The dance committee didn’t make different kinds of tickets, and they lost track of how many of each kind of ticket they sold. They know they sold a total of 500 tickets and brought in $3,135. How many Jefferson and non-Jefferson students came to the dance?

Answer 1

there were 127 non-Jefferson students who came to the dance.

Explanation:

Let J be the number of Jefferson students who came to the dance and N be the number of non-Jefferson students who came to the dance. We know that J + N = 500 and 5J + 10N = 3135.

Substituting the first equation into the second equation, we get:

5J + 10(500 - J) = 3135

5J + 5000 - 10J = 3135

-5J = -1865

J = 373

Therefore, there were 373 Jefferson students who came to the dance.

Substituting this back into the first equation, we get:

373 + N = 500

N = 500 - 373

N = 127

Therefore, there were 127 non-Jefferson students who came to the dance.