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Algebra Adventures
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Algebra Adventures
Help plan a pop-up adventure park. Use algebra to describe costs, solve puzzles and check whether the plans work. Show your working where needed.
Decode the park plans
Write an algebraic expression for each situation. Use the variable given.
1.A climbing pass costs $x. A helmet hire costs $4. Write an expression for the total cost of one pass and helmet hire.
2.Each raft holds 6 people. Write an expression for the number of people carried by r full rafts.
3.A snack stall starts with c lamingtons and sells 9. Write an expression for the number left.
Solve the challenges
Substitute the given value, or solve each equation. Include a clear method for the longer problems.
4.The park's entry fee is $7 plus $3 for each activity, a activities. Write a rule for the total cost T.
5.Using T = 7 + 3a, find the total cost when a visitor chooses 4 activities.
6.A group buys 5 identical activity bands for $60 altogether. If each band costs b dollars, write an equation and find b.
7.Solve the ticket puzzle: 3n + 5 = 26. Show the inverse operations you use.
8.A rectangular picnic area is 8 m long and w metres wide. Write an expression for its perimeter, then calculate it when w = 5.
9.Harper says 4(x + 2) = 4x + 2. Is she correct? Explain by expanding the brackets and, if useful, checking x = 3.
10.A park fundraiser earns $5 for every ticket sold, but pays $18 to hire a table. Write an expression for the profit after selling t tickets. Then find the profit for 12 tickets.
11.Create your own park situation that can be represented by 2m + 6. Explain what m and the numbers 2 and 6 represent.
2 printable pages
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