SAT Equation Questions
Revenue Problems
The SAT frequently asks systems of equations questions.
Sometimes the equations are given directly with x and y.
Other times they appear as a word problem.
These questions usually involve prices, quantities, total items, and total revenue.
We call this family of questions Revenue Problems.
We will make the problem easier by organizing the information into a SATMath800 Decoder Table.
A school store sells notebooks for $4.50 each and pens for $1.75 each.
A total of 160 items were sold.
The total revenue was $495.
How many notebooks were sold?
Pause here and try to solve it before watching the solution.
Watch the Video First
In this short whiteboard lesson, I explain how to recognize a Revenue Problem, build the SATMath800 Decoder Table, and convert the word problem into a system of equations step by step.
Watch the video first, then continue below to review the table, equations, and practice problem.
Step 1 — Decode the Problem
Before writing any equations, identify what the question is asking.
The question asks for the number of notebooks.
Now organize the information into a table.
| Notebook | Pen | |
|---|---|---|
| Price | $4.50 | $1.75 |
| Number Sold | x | y |
Turn the Table into Equations
Now that the information is organized, we can translate it into a system of equations.
First Equation — Total Items
The total number of items sold is 160.
Notebooks are represented by x and pens are represented by y.
Second Equation — Total Revenue
Each notebook costs $4.50, so notebook revenue is 4.5x.
Each pen costs $1.75, so pen revenue is 1.75y.
The total revenue is $495.
4.5x + 1.75y = 495
Solve the System Using Elimination
The question asks for the number of notebooks. That means we only need to find x. The fastest strategy is to eliminate y.
- We need x.
- The other variable is y.
- We will eliminate y.
Step 1 — Start with the System
4.5x + 1.75y = 495
Step 2 — Multiply the First Equation
The second equation has +1.75y. To cancel it, multiply the first equation by −1.75.
Step 3 — Rewrite the Equation
Step 4 — Add the Equations
4.5x + 1.75y = 495
The y terms disappear, so we can now solve for x.
Step 5 — Solve for x
x ≈ 78
The school store sold 78 notebooks.
🚀 Practice It Yourself
Now solve a very similar SAT revenue problem. Use the same SATMath800 Decoder Table strategy before looking at the solution.
A movie theater sells adult tickets for $12 and student tickets for $8.
A total of 180 tickets were sold.
The total revenue was $1,680.
How many adult tickets were sold?
| Adult | Student | |
|---|---|---|
| Price | $12 | $8 |
| Number Sold | x | y |
🧠 Finished? Check Your Solution
Step 1 — Define the Variables
y = student tickets
Step 2 — Write the System
12x + 8y = 1680
Step 3 — Eliminate y
Multiply the first equation by −8.
Step 4 — Add the Equations
12x + 8y = 1680
Step 5 — Solve for x
x = 60
Notice that the process is exactly the same as the video lesson: Decoder Table → Build the System → Eliminate the variable you do not need → Solve for the requested variable.
📚 Lesson Summary
Recognize Revenue Problems
SAT revenue problems usually give prices, quantities sold, total items, and total revenue.
Use the Decoder Table
Organize the information into a SATMath800 Decoder Table before writing any equations.
Build the System
Create one equation for the total number of items and one equation for the total revenue.
Eliminate the Unnecessary Variable
Focus on the variable the SAT asks for. Eliminate the other variable to save time on test day.
Ready for More SAT Math?
This lesson covered one of the most common SAT systems of equations word problems. At SATMath800.com you can find more 100% free SAT Math lessons, SAT-style practice questions, whiteboard video explanations, and step-by-step solutions designed for the Digital SAT.
Think Smarter. Score Higher.
Questions or Suggestions?
Did you solve the practice problem in a different way? Is there another SAT Math topic you would like to see as a SATMath800 Whiteboard Lesson?
Leave a comment below. Many future SATMath800 lessons are inspired by questions from students preparing for the Digital SAT.
— Dr. Aytekin · SATMath800
