Soup for 138: Scaling a Recipe Under Packaging Constraints
The student council has contracted to provide soup at the adults' awards evening in the school canteen on 14 March. The standard recipe serves 24 people and uses 2.4 kg of potatoes, 900 ml of vegetable stock and 300 ml of cream. Attendance is confirmed at 138 paying guests, and the council agreed after last year's event to prepare an extra 8% of portions so that nobody is turned away. Suppliers sell potatoes only in 2.5 kg bags at €3.50 each, stock only in 1 litre cartons at €1.25 each, and cream only in 500 ml tubs at €1.60 each. The council will charge the parents' association €3.20 per paying guest, and the caterer requires a 25% deposit on the total charge plus a flat €25 delivery charge, payable when the order is placed on 1 March. The council's float currently stands at €300. One member wants to order exactly the calculated quantities; another insists they should simply double every ingredient to be safe.
1. Calculate the quantities of potatoes, stock and cream that must actually be purchased, and the total ingredient cost.
Read the worked answer
Step 1 – Portions needed. 138 × 1.08 = 149.04. Portions cannot be fractional, so round up to 150.
Step 2 – Scale factor. 150 ÷ 24 = 6.25.
Step 3 – Scale each ingredient.
- Potatoes: 2.4 × 6.25 = 15 kg. Bags hold 2.5 kg, so 15 ÷ 2.5 = 6 bags exactly → 6 bags = €21.00.
- Stock: 0.9 × 6.25 = 5.625 L. Cartons are 1 L, so 5 cartons (5 L) would be 0.625 L short. Buy 6 cartons = €7.50.
- Cream: 0.3 × 6.25 = 1.875 L. Tubs are 0.5 L, so 3 tubs = 1.5 L is short. Buy 4 tubs = 2 L = €6.40.
Step 4 – Total. 21.00 + 7.50 + 6.40 = €34.90.
Note the two different rounding decisions: potatoes divide exactly, so no spare is bought, while stock and cream must be rounded up because part-units cannot be purchased. The cost per portion is 34.90 ÷ 150 ≈ €0.23.
2. The association is charged €3.20 per paying guest. Show whether the €300 float covers the 25% deposit on the total charge including the €25 delivery charge, and state the balance left.
Read the worked answer
Step 1 – Total charge. Only the 138 paying guests are charged; the 8% buffer portions are prepared but not paid for. 138 × €3.20 = €441.60.
Step 2 – Add the delivery charge. The deposit is a percentage of the total charge, so the delivery charge must be inside the calculation: 441.60 + 25.00 = €466.60.
Step 3 – Deposit. 25% of 466.60 = 466.60 × 0.25 = €116.65. (A quick check: 10% is €46.66, so a quarter is roughly 2.5 times that.)
Step 4 – Compare with the float. €300 − €116.65 = €183.35 remaining.
The deposit is comfortably covered, but the €183.35 is already committed: €34.90 of it must be held back for ingredients, leaving about €148 for the balance of the caterer's charge. Treating the whole €300 as available spending money would be the error the exam is testing for.
3. A member proposes doubling all ingredient quantities. Evaluate this proposal and state what you would actually order.
Read the worked answer
Doubling the scaled quantities means ordering 12 bags of potatoes (30 kg), 12 cartons of stock (12 L) and 8 tubs of cream (4 L).
- Cost: 12 × 3.50 = €42.00; 12 × 1.25 = €15.00; 8 × 1.60 = €12.80 → €69.80, exactly double the €34.90 required.
- Waste: 30 kg of potatoes against 15 kg needed leaves 15 kg, roughly €21 of food, and the canteen has no cold store for that volume. Cream is perishable and cannot be carried over.
The purpose of the 8% allowance was precisely to absorb unexpected demand; it has already been built into the 150 portions. Doubling on top of that is double-counting the safety margin.
A defensible order is the calculated minimum plus one spare carton of stock only (€1.25, shelf-stable, and the ingredient most likely to be spilled or boiled down). Potatoes and cream are bought to the rounded figure. The judgement being tested is that a contingency should be cheap and storable, not simply a blanket multiplier.