Juice for the Robotics Showcase
The robotics club needs at least 96 fl oz of juice for a 24-student showcase; they plan 4 oz per student. Store A sells 12-oz bottles for $2.40 each. Store B sells 20-oz bottles for $3.60 each and takes 15% off the entire purchase only when the subtotal reaches $20 or more. Store C sells a 64-oz jug for $7.50. The club's budget is $20, and the advisor will not store opened juice overnight, so any leftover is discarded.
1. Determine the cheapest way to meet the 96 fl oz minimum within the $20 budget. Support your choice with unit prices and totals, and explain why Store B's discount does not win.
Read the worked answer
Unit prices: A = $2.40 ÷ 12 = $0.20/oz; B = $3.60 ÷ 20 = $0.18/oz; C = $7.50 ÷ 64 ≈ $0.117/oz.
Meeting 96 oz at each store:
- A: 8 bottles = 96 oz, 8 × $2.40 = $19.20 (under budget).
- B: 5 bottles = 100 oz, 5 × $3.60 = $18.00 - subtotal is under $20, so no discount applies.
- C: 1 jug is only 64 oz (short), so 2 jugs = 128 oz = $15.00.
The discount trap: to reach the $20 subtotal at B, the club must buy 6 bottles ($21.60), which drops to $21.60 × 0.85 = $18.36. That is within budget, but it costs $0.36 more than the undiscounted 5-bottle purchase. A percentage off a larger basket can still leave a larger total.
Answer: buy 2 jugs at Store C for $15.00, which meets the minimum, stays under budget, and leaves $5 for cups.
2. The advisor adds a rule: no more than 8 fl oz may be discarded. Re-evaluate the three options and explain what changed.
Read the worked answer
Apply the leftover limit: 96 oz needed, so the largest acceptable purchase is 104 oz.
- A: 8 bottles = 96 oz, 0 oz leftover, $19.20 → allowed.
- B: 5 bottles = 100 oz, 4 oz leftover, $18.00 → allowed. (6 bottles, 120 oz, is now disqualified.)
- C: 2 jugs = 128 oz, 32 oz leftover, $15.00 → disqualified, because 32 oz exceeds the 8 oz limit.
Answer: Store B, 5 bottles, $18.00.
What changed: the objective is no longer "lowest cost per ounce." It is "lowest total cost subject to two constraints - at least 96 oz and at most 104 oz." Store C still has the best unit price, so a student ranking by unit price alone would keep choosing it and violate the new rule. The lesson is that unit rate identifies efficiency, not the best decision, once hard constraints are in play.