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Linear Equations Word Problems

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Linear Equations Word Problems

📊 Part 1: Forming Equations

1. Sarah has $75 to spend at the mall. She buys 3 items that cost $x each and has $21 left. Which equation represents this situation?

75 - 3x = 21

75 + 3x = 21

3x - 75 = 21

75 - x = 21

2. A recipe for 6 people uses 450g of flour. How much flour (f) is needed per person? Choose the correct equation:

6f = 450

f + 6 = 450

450f = 6

f - 6 = 450

3. Tom drives at 80 km/h for t hours and travels 240 kilometres. Which equation can be used to find t?

80 + t = 240

80t = 240

80 - t = 240

t ÷ 80 = 240

✏️ Part 2: Solve and Explain

4. Jessica has $120 for school supplies. She buys 5 notebooks at $n each and has $45 remaining.
a) Write an equation to represent this situation: ________________
b) Solve for n and show your working:
5. A pizza recipe serves 8 people and uses 600g of cheese. How much cheese is needed for 12 people?
a) Let x = grams of cheese needed. Write an equation: ________________
b) Solve and show your steps:
6. A train travels at a constant speed of 90 km/h. If it takes 2.5 hours to reach its destination, how far did it travel?
a) Write an equation using d for distance: ________________
b) Calculate the distance:

🎯 Part 3: Real-World Applications

7. Marcus is saving money for a new bike that costs $350. He already has $80 and plans to save $15 each week.
a) Write an equation to find how many weeks (w) he needs to save: ________________
b) Solve the equation and explain what your answer means in context:
8. A mobile phone plan costs $25 per month plus $0.30 for each text message sent. If Priya's monthly bill was $37, how many text messages did she send?
a) Set up the equation: ________________
b) Solve and verify your answer makes sense:
9. Create your own word problem that can be solved using a linear equation. Include the problem, equation, and solution:

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