Instructions
This worksheet challenges you to become a Variable Investigator. You will read real-world scenarios and translate them into mathematical equations using variables. Follow these steps for each section:
- Read the word problem carefully.
- Define the unknown quantity using a variable (usually $x$ or the first letter of the unknown thing).
- Write the algebraic equation that represents the problem.
- Solve the equation and state your final answer in a complete sentence.
Section 1: Defining the Unknown (Scaffolding)
Before solving, you must clearly define what your variable represents. Complete the table below. (The first one is done for you.)
| Word Problem Scenario | What is the unknown quantity? | Choose a Variable and Definition (Example: $x$ = Cost of shirt) |
|---|---|---|
| A concert hall holds 450 people. If 120 tickets are already sold, how many tickets ($t$) are left? | The number of tickets remaining. | $t$ = Number of tickets remaining |
| Mark earned $35 by mowing lawns. If he saves $5 per week ($w$), how long will it take him to save $140 total? | The number of weeks Mark needs to save. | $w$ = ____ |
| A recipe calls for 4 cups of flour. If I have already added $c$ cups, and need 1.5 more cups, how much did I start with? | The amount of flour already added. | $c$ = ____ |
| Julia ran 3 miles less than her goal ($g$) distance. If she ran 8 miles, what was her goal? | Julia's goal distance for running. | $g$ = ____ |
| Six friends split the cost ($c$) of a $72 video game equally. How much did each friend pay? | The amount each friend paid. | $c$ = ____ |
| A subscription service charges $15 plus $0.50 per downloaded episode ($e$). | The number of episodes downloaded. | $e$ = ____ |
Section 2: One-Step Equation Missions
For each problem, define the variable, write the equation, and solve.
Mission 1: The Library Fines
Leo had a $4.50 library fine. He paid some of the fine using change he found, and now his remaining fine is $1.25. How much change ($c$) did Leo find and use?
- Define the variable: $c$ = ____
- Write the equation:
- Solve the equation:
- Final Answer Sentence:
Mission 2: The Cake Division
Mrs. Diaz bought a large cake for her class. She cut it into 24 equally sized pieces. If 18 pieces were eaten, how many pieces ($p$) are left?
- Define the variable: $p$ = ____
- Write the equation:
- Solve the equation:
- Final Answer Sentence:
Mission 3: The Hiking Trail
Maria hiked 4 times the distance that Ben hiked. If Maria hiked 10 miles, how many miles ($m$) did Ben hike?
- Define the variable: $m$ = ____
- Write the equation:
- Solve the equation:
- Final Answer Sentence:
Section 3: Two-Step Equation Challenges
These problems require two operations to solve. Use $x$ to represent the unknown.
Challenge 1: The Arcade Budget
Jamie went to the