Weighted bundle accounting
Fruit Bundle Mystery
Two fruit baskets seem to make a simple bargain, but combining their selling rates can lose tokens. Your group acts as a pretend stall team and reconstructs every batch. This is a paper arithmetic game using fictional tokens, with no purchase or money required.
Work together, or form two small teams and rotate the writer. Age and time are planning estimates; choose the reading and arithmetic support that suit your group.
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Print one player sheet per team and one host guide for the adult. Both are black and white. Keep the host guide separate to avoid revealing answers. No cutting, folding, special props or account required.
No printer? Copy the grids and prompts onto plain paper. The full activity is below; hints and answers stay closed until selected.
Set up and rules
Bring pencils, an eraser and one sheet of paper per team. Print at 100% / actual size. Read the rules together, try the warm-up, work through two rounds, and finish with the final challenge.
- Basket A contains 30 pretend oranges bought at 2 oranges per token. Basket B contains 30 bought at 3 per token.
- The stall sells all 60 oranges in groups of 5 for 2 tokens per group. There are no other costs, leftovers or partial sales.
- Keep quantities, group prices and total tokens in separate columns. Do not add unit rates unless the quantities used justify it.
Warm-up: what did the fruit cost?
Find the cost of each basket and the combined cost.
Hint 1
Calculate each basket separately.
Hint 2
Divide 30 by the number of oranges bought for one token.
Check the answer and reasoning
A costs 15 tokens; B costs 10 tokens; total cost is 25.
30÷2=15 and 30÷3=10. Add costs, not the denominators of the rates.
Round 1: count the sale groups
All 60 oranges sell in groups of 5 for 2 tokens. How many groups, how much revenue, and what gain or loss?
Hint 1
First count groups, then price the groups.
Hint 2
Compare 24 received with 25 spent.
Check the answer and reasoning
12 groups; 24 tokens received; loss of 1 token.
60÷5=12 groups; 12×2=24 tokens. The fruit cost 25, so 24−25=−1.
Round 2: follow both baskets
For each of the first 10 sale groups, take 2 oranges from A and 3 from B. What remains after these 10 groups, and what did those remaining oranges originally cost?
Hint 1
Track each basket independently.
Hint 2
The last 10 oranges all came from A.
Check the answer and reasoning
10 oranges remain in A; none remain in B. The remaining fruit cost 5 tokens.
Ten groups consume 20 from A and 30 from B. A has 30−20=10 left, bought at 2 per token, so those 10 cost 5.
Final: repair only the last two groups
Keep the first 10 groups at 2 tokens each. The last 10 oranges form two more groups of 5. Charge the same price for both final groups. What price per group recovers exactly the original 25-token cost? Half-token prices are allowed in this pretend game.
Hint 1
Find the amount still needed after receiving 20.
Hint 2
Divide the remaining 5 tokens across 2 equal groups.
Check the answer and reasoning
2.5 tokens per final group.
The first 10 groups bring 20 tokens. Recovering the original 25 needs 5 more; split equally across two groups, that is 2.5 each. Charging 2 each would bring only 4.
Offer support
Draw 30 short marks per basket, or work in groups of six. An adult can perform division while players decide what each number represents. Keep the cost and sale calculations on different lines.
Finish together
Finish by explaining the final repair in plain words: equal basket quantities are not the same as selling two oranges from A and three from B in every group.
If you disagree about an answer, return to the stated rules and compare the written steps. Keep the activity cooperative; a hint is part of play, and nobody needs to be eliminated.
Choose another paper puzzle · Try a shorter group game · Find a full mystery adventure