The Reunion Juice Budget
The reunion committee for the Ellis family needs to serve 150 mL of orange juice to each of 80 guests at a Sunday picnic. That is exactly 12 L. Three stores advertise these prices, and 15% VAT is added at the till to every price shown. Store A: 1 L cartons at $4.25 each, with a 'buy 4, get 1 free' offer applied to every group of 4 paid cartons. Store B: 2 L bottles at $7.80 each, no offer. Store C: 1.5 L bottles at $5.70 each, with 10% off the whole juice bill when 6 or more bottles are bought. The committee has a budget of $85 and a refrigerator that can hold at most 18 L. They want to buy at least 12 L and avoid more than 2 L of leftovers because opened juice spoils. Two committee members disagree: one says Store A is cheapest because of the free cartons; the other says Store C is cheapest because of the percentage discount.
1. Calculate the effective price per litre before VAT for each store when buying exactly the quantity needed to reach at least 12 L. Show the pack combinations you use.
Read the worked answer
Store A: the offer is 1 free carton for every 4 paid. To receive 12 L (12 cartons), pay for 10 and receive 2 free. Cost before VAT = 10 × $4.25 = $42.50; per litre = $42.50 ÷ 12 = $3.54 (3 d.p.).
Store B: 6 × 2 L = 12 L; cost = 6 × $7.80 = $46.80; per litre = $3.90.
Store C: 8 × 1.5 L = 12 L; cost before discount = 8 × $5.70 = $45.60; 10% discount = $4.56; cost = $41.04; per litre = $3.42.
So before VAT, C has the lowest unit price, then A, then B.
2. Which store should the committee choose if they want the lowest total amount paid including VAT? Show the final cost and check it against the $85 budget.
Read the worked answer
Add 15% VAT to each total.
A: $42.50 × 1.15 = $48.875, which rounds to $48.88. B: $46.80 × 1.15 = $53.82. C: $41.04 × 1.15 = $47.196, which rounds to $47.20.
Store C is cheapest. All three give exactly 12 L, so there is no leftover. The $85 budget is met with $37.80 to spare ($85 − $47.20). The 'free cartons' at A do not make it cheapest because the base carton price is high; the 10% discount at C is worth more.
3. Suppose the committee decides to buy 14 L to allow for a little extra. Recalculate the cheapest option under the 18 L fridge limit and the 'no more than 2 L leftover' rule.
Read the worked answer
Target 14 L.
A: to receive 14 cartons, pay for 12 and receive 3 free = 15 L. Cost before VAT = 12 × $4.25 = $51.00; with VAT = $58.65; leftover 1 L. B: 7 × 2 L = 14 L; cost = 7 × $7.80 = $54.60; with VAT = $62.79; no leftover. C: 10 × 1.5 L = 15 L; cost before discount = $57.00; after 10% = $51.30; with VAT = $58.995, which rounds to $59.00; leftover 1 L.
Now A is cheaper by $0.35 compared with C, and both are within the 18 L fridge limit and the 2 L leftover rule. Choose A.