Question 130·Easy·Linear Equations in Two Variables
At a school play, adult tickets cost $15 each and student tickets cost $8 each. The total amount collected from ticket sales was $360. Which equation represents the possible numbers of adult tickets, , and student tickets, , that were sold?
For word problems that ask for an equation, start by clearly labeling the variables and writing a separate expression for each part of the situation (here, money from adult tickets and money from student tickets). Make sure each variable is multiplied by the correct unit price, then combine those expressions in the way the problem describes (usually adding different parts and setting the sum equal to the given total). Finally, compare your constructed equation to the answer choices, checking that coefficients, variables, and the equals sign all match the story and the units (dollars vs. tickets).
Hints
Match each variable to its ticket type
Ask yourself: Which variable is the number of adult tickets, and which is the number of student tickets? Keep that straight when you connect each variable to a price.
Turn words into expressions
Write an algebraic expression for the total money from adult tickets and another expression for the total money from student tickets, using the given prices and variables.
Connect the expressions to the total
Once you have expressions for the money from adult and student tickets, how should you combine them to represent the total money collected, $360?
Desmos Guide
Choose a simple valid ticket combination
Imagine the school sold only adult tickets and no student tickets. Since each adult ticket is $15 and the total is $360, divide $360 by $15 to see that 24 adult tickets would make $360, so one realistic combination is , .
Test each equation with the chosen values
In Desmos, for each answer choice, type its left-hand side as an expression (for example, 8x + 15y for choice A), then use the "Add Table" feature and enter and in the table. Desmos will show the resulting value of the expression.
Identify which equation fits the situation
Look at which expression equals $360 when and . The answer choice whose left-hand side evaluates to 360 for this realistic ticket combination is the equation that correctly represents the situation.
Step-by-step Explanation
Translate the variables and prices
The problem defines as the number of adult tickets and as the number of student tickets.
- Each adult ticket costs $15.
- Each student ticket costs $8.
So the money from adult tickets will depend on , and the money from student tickets will depend on .
Write expressions for money from each ticket type
If each adult ticket is $15 and there are adult tickets, the total money from adult tickets is .
If each student ticket is $8 and there are student tickets, the total money from student tickets is .
These two expressions represent the dollar amounts from each group of tickets.
Combine the parts to match the total amount
The total money collected is the sum of the adult-ticket money and the student-ticket money, and this sum must equal $360.
So we add the two expressions and set them equal to $360:
This matches answer choice D, which is the equation that correctly represents the situation.