Question

A group of more than two and fewer than twenty students all paid the same whole dollar amount for a ticket to a concert. If the total cost was $493, how many students were in the group?

Answer 1

A group of more than two and fewer than twenty students all paid the same whole dollar amount for a ticket to a concert. If the total cost was $493, how many students were in the group?

Let n be the number of students.

Let p be the price of a ticket.

Then    2 < n < 20

And      np = 493

All we need to do now is find the integer factors of 493 such that one of the factors will satisfy the inequality for n.

493 has two prime factors, 17 and 29  (gotten by trial and error)

Since 29 is greater than 20 then it cannot be n.

So n must be 17

Answer: there were 17 students in the group