Grades Grade 7 Expressions & EquationsModeling Real-World Situations with Equations

Modeling Real-World Situations with Equations

✏️ Expressions & Equations

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Modeling Real-World Situations with Equations

Translate word problems into equations, solve them, and interpret the solution.

Real-world problems require identifying the unknown quantity, assigning a variable, building an equation from the relationships described, solving it, and checking whether the answer makes sense in context.

🎟️Concert ticket problem

Admission tickets cost $12 each. A service fee of $5 is charged per order. If you spent $65 total, how many tickets did you buy?

Let t = number of tickets.
12t + 5 = 65
12t = 60
t = 5 tickets

12t + 5 = 65 \Rightarrow 12t = 60 \Rightarrow t = 5

Problem-solving strategy:

1Read carefully — identify what is unknown

2Assign a variable to the unknown (e.g., let n = number of items)

3Translate the relationships into an equation

4Solve using inverse operations

5Check: substitute your answer back into the original equation

6Interpret: does the answer make sense? (Can you buy 5 tickets? Yes.)

🚗Distance / speed / time

Two towns are 195 miles apart. A car has already driven 45 miles. If the car travels at 50 mph, how many more hours until it arrives?

50h + 45 = 195 → 50h = 150 → h = 3 hours

50h + 45 = 195 \Rightarrow 50h = 150 \Rightarrow h = 3

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Remember This!

Write out the equation BEFORE solving. Students who skip straight to arithmetic often miss a step. The equation is your roadmap.

✏️ Try It!

A phone plan charges $25/month plus $0.10 per text. Your bill was $32.50. How many texts did you send?

Practice with CalcVerse

🎯Linear Equation Solver 🍽️Tip & Bill Splitter

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