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?
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.