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Algebra Scavenger Hunt
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Name:Date:
Algebra Scavenger Hunt
Solve each post-office clue to uncover the next code. Show your working and include units where they are needed. You can complete the clues in any order.
Collect the clues
Each clue gives you a number or expression for your scavenger-hunt record.
1.Clue 1 — Parcel shelf: Rawiri packs identical small parcels. Three parcels and a $3 packing fee cost $48 altogether. Let p be the cost of one parcel. Write an equation and find p.
2.Clue 2 — Stamp drawer: Ana buys x $2 stamps and (x + 3) $3 stamps. The stamps cost $27 altogether. Which equation represents the situation?
- 2x + 3(x + 3) = 27
- 2(x + 3) + 3x = 27
- 2x + 3x + 3 = 27
- 5x + 3 = 27
3.Clue 3 — Envelope scale: A stack of four identical envelopes and a parcel label with a mass of 2.40 g weigh 10.40 g altogether. If e is the mass of one envelope in grams, solve 4e + 2.40 = 10.40.
4.Clue 4 — Sorting machine: Solve 5(2x − 3) = 35. Show the first step you use, then give the value of x.
5.Clue 5 — Parcel cage: A rectangular parcel has width x cm and length (x + 4) cm. Its perimeter is 36 cm. Write and solve an equation to find its width and length.
Decode the final code
Use algebra to crack the last set of post-office puzzles.
6.Clue 6 — Label printer: Simplify the expression 3(2n − 4) + 5. Choose the simplified expression.
- 6n − 7
- 6n − 12
- 6n + 1
- 5n − 7
7.Clue 7 — Counter code: Solve 2(3x + 1) = 4x + 14. What number should Ana enter as the code?
8.Clue 8 — Match each equation to its solution. Write the correct letter beside each equation.
- A. 3x + 5 = 20
- B. 4(x − 2) = 8
- C. 2x + 7 = 13
- 2. x = 3
- 1. x = 4
- 3. x = 5
9.Final challenge — Ari says the equation 2(x + 5) = 2x + 10 has no solution because the x terms cancel. Is Ari correct? Explain what happens when you simplify both sides.
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