   SEARCH HOME Math Central Quandaries & Queries  Question from Diane, a student: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by$5. How many students attended the get-together? Hi Diane.

Let p equal the number of people who planned to come originally and c be the planned cost per person.

So the plan was that (p) people would each pay (c) dollars to cover the $500 budget. (p)(c) = 500. Since 5 people failed to show up and pay anything, the$500 had to come from (p - 5) people.

The cost per person was $5 higher than originally planned, so it was (c + 5) dollars. Thus (p - 5) people each paid (c + 5) dollars in order to cover the$500 budget.

(p - 5)(c + 5) = 500.

So you have these two equations with two unknowns and you are asked to find the value of (p - 5), the number of people who showed up.

From here, I would use the "substitution method" to replace the c in the second equation by its value from the first equation and solve for p.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.