Math CentralQuandaries & 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.

Stephen La Rocque.

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