Concept 5
Build a system from a word problem and interpret the solution.
Write one equation per condition, solve the system, and interpret the answer in context.
Core Idea
Assign a variable to each unknown quantity, write one equation per condition in the problem, solve the system, then translate the numbers back into the context.
Understanding
Write one equation for each condition. Most SAT systems stories give you two clues: a total count and a total value.
- Define two variables for the unknown quantities.
- Turn each condition into an equation.
- Solve the system, then answer the question in context.
The setup is usually the real work. Once the equations are written correctly, the algebra is routine.
Step by Step
- Identify two unknowns and define variables (e.g.,
𝑎 𝑐 - Write one equation from the first condition (e.g., total count:
𝑎 + 𝑐 = 2 0 0 - Write a second equation from the second condition (e.g., total revenue:
1 2 𝑎 + 8 𝑐 = 2 1 6 0 - Solve the system using substitution or elimination.
- Re-read the question — answer exactly what was asked, in context.
Misconceptions
- Assigning variables but mixing them up mid-problem — calling
𝑥 - Finding both variables correctly but answering with the wrong one because the question asked for the other quantity.
- Writing two equations that are actually the same relationship restated, which gives infinitely many solutions instead of a unique answer.
Question
Worked Example
A store sells notebooks for $5 each and pens for $2 each. A customer buys 10 items for a total of $38. How many notebooks did the customer buy?
Select an answer to see the explanation