Start. Fictional paper strips are sold as A: 8 strips for $3.20 and B: 12 strips for $4.20. Find $/strip: $0.40 and $0.35. For exactly 24 strips with whole packs and no fees, A costs $9.60 and B costs $8.40. Now say B adds a $2 handling fee. Recalculate B's total as $10.40. Ask why the smaller unit price no longer decides the cheaper complete order.
Route 24A · Whole packs and leftovers
A fictional label offer sells 5 labels for $1.80; B sells 8 labels for $2.72. You need at least 18 labels. Packs cannot be split. Calculate each unit price, number of packs, cost and leftovers. Choose the cheaper sufficient order. State the assumption that prices include every fee.
Teacher next move: A $0.36/label, four packs 20, $7.20, two spare; B $0.34/label, three packs 24, $8.16, six spare. A is cheaper for this need even though B's unit price is smaller.
Route 24B · Find the point where a decision changes
An imaginary diagram service charges A $2 per page with no fee, or B $1 per page plus a $6 start fee. Pages are whole positive numbers. Make a table for 4, 6 and 8 pages, find the equal-cost quantity, then write a decision rule for whole positive quantities. Show where the fee enters the calculation.
Teacher next move: A 8/B 10 at 4; both 12 at 6; A 16/B 14 at 8. A cheaper for 1–5, equal 6, B cheaper ≥ 7. The proportional $/page rate is only part of B's total model.
Route 24C · Ask for the missing condition
One fictional card says “$0.30 per token”. Another says “$2.40 for a pack of 10”. You need 16 usable tokens. List what you must know before a fair decision: whether single tokens can be bought, whether packs split, whether fees exist and whether tokens are interchangeable. Then solve under these stated conditions: the first sells singles with no fee; the second sells whole packs with no fee; every token is usable. Explain how a different condition could change the answer.
Teacher next move: singles 16 cost $4.80; two packs 20 cost $4.80, four spare. Equal stated cost; a learner can choose based on leftover usefulness. A new fee or maximum quantity would change the model.
Close: name the useful comparison, then one condition the comparison needs.