Question 122·Medium·Linear Equations in One Variable
The International Club paid a fixed venue rental fee of $175 for its annual dinner. They collected an equal admission fee from each of the 50 people who attended. After paying the rental fee, the club had $325 left for future activities.
What was the admission fee, in dollars, that each attendee paid?
(Express the answer as an integer)
For word problems about money collected, expenses, and leftover amounts, first define a variable for the unknown (like the price per ticket). Write an equation that starts with the total collected (number of people × price), then subtract fixed costs to equal the leftover amount. Carefully check whether each amount should be added or subtracted, then solve the resulting one-variable linear equation step by step. This keeps the work organized and reduces mistakes with the operations.
Hints
Identify the unknown
Let represent the admission fee each person paid. Ask: how much money did the club collect in total from 50 people?
Relate total collected, cost, and leftover
Write an expression for the total admissions money, then subtract the $175 rental fee. That result should equal the $325 the club had left.
Solve the equation step by step
Once you have your equation, first isolate the term, then divide to find .
Desmos Guide
Express the total admissions money
In Desmos, type y = 50x - 175 to represent the money remaining after paying the rental fee, where is the admission fee per person.
Find the intersection with the leftover amount
On a new line, type y = 325. Click on the intersection point of the two lines. The x-coordinate is the admission fee per person.
Step-by-step Explanation
Translate the situation into an equation
Let be the admission fee, in dollars, that each of the 50 people paid.
- Total money collected from admissions is .
- The club paid a fixed rental fee of $175.
- After paying this, they had $325 left.
So the money after paying the rental fee is:
Solve the equation for x
We now solve the linear equation:
First, add to both sides to undo the subtraction:
Compute the sum on the right:
Find the admission fee per person
Now divide both sides by to solve for :
So the admission fee each attendee paid was $10 dollars.