Flapjack Recipe Scaling and Pack Cost
The cooking club at a school has a recipe for 24 flapjacks: 300 g oats, 180 g butter, 150 g golden syrup and 120 g sugar. They need 150 flapjacks for a charity stall. Ingredients are sold only in these pack sizes: oats 1 kg for £1.80, butter 250 g for £1.60, golden syrup 340 g for £1.20, and sugar 1 kg for £0.90. The club wants to allow 10% extra of every ingredient for tasting and waste, and it must buy whole packs with no sharing or returning leftovers. The stall budget for ingredients is £25. A parent has offered to pay for any ingredients over £20, but only if the club can show the exact pack list and cost. The club also wants to know whether the 10% allowance changes the number of packs bought compared with using the recipe exactly.
1. Scale the recipe to 150 flapjacks, including the 10% extra allowance. Give the required mass of each ingredient before rounding to packs.
Read the worked answer
Scale factor = 150 ÷ 24 = 6.25. Oats: 300 × 6.25 = 1875 g; with 10% extra = 1875 × 1.10 = 2062.5 g. Butter: 180 × 6.25 = 1125 g; extra = 1237.5 g. Syrup: 150 × 6.25 = 937.5 g; extra = 1031.25 g. Sugar: 120 × 6.25 = 750 g; extra = 825 g.
2. Using whole packs only, list the packs needed and calculate the total cost. Does the cost stay within the £25 budget and within the parent's £20 threshold?
Read the worked answer
Oats: 2062.5 ÷ 1000 = 2.0625, so 3 × 1 kg packs = £5.40. Butter: 1237.5 ÷ 250 = 4.95, so 5 packs = £8.00. Syrup: 1031.25 ÷ 340 = 3.033..., so 4 packs = £4.80. Sugar: 825 ÷ 1000 = 0.825, so 1 pack = £0.90. Total = 5.40 + 8.00 + 4.80 + 0.90 = £19.10. This is within the £25 budget and also below £20, so the parent's over-£20 offer is not triggered.
3. Compare this with buying exactly the scaled recipe without the 10% allowance. Which packs change, and what is the difference in cost?
Read the worked answer
Without the 10% allowance: oats 1875 g needs 2 × 1 kg packs (£3.60); butter 1125 g needs 5 packs (£8.00); syrup 937.5 g needs 3 × 340 g packs because 3 × 340 = 1020 g (£3.60); sugar 750 g needs 1 pack (£0.90). Total = 3.60 + 8.00 + 3.60 + 0.90 = £16.10. The 10% allowance adds one oat pack and one syrup pack, costing £3.00 more. The club must judge whether the £3.00 insurance against waste and tasting is worth it; the budget allows either choice, but the parent's £20 threshold is still not reached in either case.