Modelling with systems

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What this lesson covers

  • Define the variables in words.
  • Each fact gives one equation.
  • Answer in context.
Worked example

Tickets

  • 120 tickets are sold for $1240. Adults pay $15 and children pay $8.
  1. a + c = 120
  2. 15a + 8c = 1240
  3. 15a + 8(120 − a) = 1240
  4. 7a = 280
  5. 40 adults and 80 children

Common mistakes

  • Writing x and y with no meaning given.
    Say what each letter stands for.
  • Giving x = 40 as the final answer.
    Finish in words, with the units of the story.

Your turn

  • 1. 3 pens and 2 rulers cost $8, and 1 pen and 1 ruler cost $3. Find each price.
Show answer

1. Pens cost $2 and rulers cost $1

Summary

What to take away

  • Name the unknowns first.
  • One fact, one equation.

More in AS 91269

Simultaneous linear equationsNotesA line and a curveNotesWhat the solutions meanNotesModelling with systemsNotes

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