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Algebraic Modelling Real-World

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Algebraic Modelling Real-World

Students solving real-world problems with algebra

🎯 WALT: We Are Learning To

Today we are learning to:

  • Use algebraic expressions to model real-world situations
  • Justify our choice of algebraic representation
  • Interpret solutions in context

🎬 Part 1: Cinema Challenge

1. Movie tickets cost $12 each, plus a $5 booking fee. Which expression shows the total cost for x tickets?

12 + 5x

12x + 5

17x

12 + 5

2. A taxi charges $4.50 base fare plus $2.20 per kilometre. Write an expression for the total cost of a trip that is k kilometres long.
3. Sarah reads 25 pages per day plus an extra 10 pages on weekends. Write an expression for total pages read in d days if there are 2 weekend days included.
4. Which real-world situations could be modelled by the expression 3n + 15? (Check all that apply)

Buying n items at $3 each plus $15 delivery

Working n hours at $15/hour plus $3 bonus

Paying $15 membership plus $3 per visit for n visits

Buying 15 items at $3 each plus n extra items

🏪 Part 2: Design Your Own Model

5. A phone plan costs $30 per month plus $0.50 for each text message over 100 free texts.

a) Write an expression for the monthly cost if you send t extra texts (over the 100 free): ________________

b) Calculate the cost if you send 80 extra texts: $________________

c) Explain why your expression makes sense for this situation:

6. Create your own real-world scenario that could be modelled by the expression 8x + 20.

Scenario:

What does x represent? ________________

What does the 8 represent? ________________

What does the 20 represent? ________________

7. A school fundraiser sells chocolates for $4 each. The class needs to pay $50 for supplies.

a) Write an expression for the profit if they sell c chocolates: ________________

b) How many chocolates must they sell to break even (profit = $0)? ________________

c) Justify your answer using your algebraic expression:

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