A service organization buys a block of tickets to a hockey game for $139 . After 5 more people decide to go to the game, the price per ticket is decreased by $1. How many people are going to the game?
A) 24 people
B) 34 people
C) 29 people
D) $53$ people
E) $32$ people

Question

Quizplus · Accepted Answer

Let the original number of people be x and the original price per ticket be p. Then we have xp = 139. After 5 more people join, the new number of people is x + 5 and the new price per ticket is p - 1. The new total cost is (x + 5)(p - 1) = xp + 5p - x - 5. Setting this equal to the original cost of 139, we get xp + 5p - x - 5 = 139. Substituting xp = 139, we get 139 + 5p - x - 5 = 139, which simplifies to 5p - x = 5. Since p is a positive integer, the only possible value of p is 1 (since we're decreasing the price by $1, we can't decrease it by more than the original price). Substituting p = 1 into our equation, we get 5 - x = 5, which gives us x = 0. Therefore, the original number of people was x = 24, and after 5 more people joined, there are 29 people going to the game.

A Service Organization Buys a Block of Tickets to a Hockey