Two Batter Suppliers for the Pancake Breakfast
The junior class is hosting a pancake breakfast, and the advisor has asked you to choose between two suppliers for the batter mix. The plan calls for 30 pounds of mix. Vendor A sells 48-ounce boxes for $5.85 each and offers 15% off the entire order if the club orders at least 8 boxes. Vendor B sells 40-ounce boxes for $4.60 each and runs a "buy 4, get 1 free" promotion that applies only to complete groups of five boxes; any boxes beyond a complete group are paid in full. Both vendors' quoted prices already include tax and delivery, and both require whole-box purchases. A parent volunteer has told the advisor that Vendor B is "obviously cheaper because the box costs less," but a second volunteer points out that the boxes are different sizes and that the free-box deal depends on how many boxes end up being ordered. The advisor wants a written comparison before signing anything, including what happens if the kitchen wastes about 10% of the batter during the morning rush.
1. Compute each vendor's price per ounce and per pound. Which is cheaper per unit, and by how much?
Read the worked answer
Convert to a common unit before comparing.
- Vendor A: $5.85 ÷ 48 oz = $0.121875/oz ≈ $0.122/oz. Per pound: $0.121875 × 16 = $1.95/lb.
- Vendor B: $4.60 ÷ 40 oz = $0.115/oz. Per pound: $0.115 × 16 = $1.84/lb.
Vendor B is cheaper by about $0.007 per ounce, or $0.11 per pound (roughly 5–6%). The first volunteer compared $4.60 with $5.85, which are prices per box, not per unit; the smaller box at the lower price is still the better buy per ounce.
2. What is the total cost from each vendor for the 30 pounds needed? Show how each discount rule works and whether it changes the ranking.
Read the worked answer
30 lb × 16 = 480 oz needed.
Vendor A: 480 ÷ 48 = 10 boxes exactly. 10 × $5.85 = $58.50. Ten boxes clears the 8-box threshold, so the 15% applies: $58.50 × 0.85 = $49.725 ≈ $49.73.
Vendor B: 480 ÷ 40 = 12 boxes exactly. The free-box rule applies only to complete groups of five: 12 boxes = 2 complete groups (10 boxes, pay for 8) plus 2 boxes paid in full = 10 paid boxes. 10 × $4.60 = $46.00.
Vendor B is cheaper by $3.73, so the ranking holds at 30 lb. Notice that B's entire advantage comes from the promotion: without it, 12 boxes would cost $55.20. The discount structures matter more than the shelf price here.
3. If the kitchen expects 10% waste, so 33 pounds must be purchased, does the answer change? Show the box counts and totals.
Read the worked answer
33 lb × 16 = 528 oz.
Vendor A: 528 ÷ 48 = 11 boxes exactly. 11 × $5.85 = $64.35; with 15% off: $64.35 × 0.85 = $54.6975 ≈ $54.70.
Vendor B: 528 ÷ 40 = 13.2, so 14 whole boxes. 14 = 2 complete groups (pay for 8) plus 4 paid = 12 paid boxes. 12 × $4.60 = $55.20.
The ranking flips: Vendor A is now cheaper by $0.50. The cause is the rounding penalty - B must round 13.2 up to 14 boxes, and only 10 of those 14 are discounted. With whole-package purchasing, cost cannot be scaled linearly from the per-unit price; it has to be recomputed at the actual quantity.