Mathematics • Year 8 • Unit 1 • Lesson 14
Best Buy at the Supermarket
Use unit prices like a real shopper: comparing pasta, cordial, cereal, dishwashing liquid and bulk rice. Then explain why “family size” isn't always the better deal.
1. Word problems
Each problem uses the idea that the lowest unit price is the better buy. Show your working — a single final answer with no working only earns half marks.
1.1 — Cordial bottles. Mia is choosing cordial. The 2 L bottle is $\$5.00$. The 1.5 L bottle is $\$3.60$.
(a) Find the unit price per L for each bottle.
(b) Which is the better buy?
(c) Mia comments “the bigger bottle is always cheaper per L”. Is she right in this case? 3 marks
1.2 — Three brands of pasta. Brand A: 500 g for $\$2.50$. Brand B: 1 kg for $\$4.80$. Brand C: 750 g for $\$3.90$.
(a) Find the unit price per kg for each brand.
(b) Rank them from cheapest to most expensive per kg.
(c) If you have $\$10$, which brand gives you the MOST pasta (in g)? 4 marks
1.3 — Dishwashing liquid duel. A 750 mL bottle costs $\$5.25$. A 1.5 L bottle costs $\$9.00$.
(a) Find the unit price per 100 mL for each.
(b) Which is cheaper per 100 mL?
(c) How much do you save per 100 mL by choosing the cheaper option? 3 marks
1.4 — Cereal showdown. 250 g box for $\$4.00$ vs 400 g box for $\$5.60$ of the SAME cereal.
(a) Find the unit price per 100 g for each.
(b) Which is cheaper per 100 g?
(c) For a family that gets through 1 kg of cereal a week, what is the cheapest weekly cost (using the cheaper option, buying enough boxes)? 3 marks
1.5 — Bulk rice trip. An online wholesaler sells rice in three sizes. 5 kg bag: $\$22$. 10 kg bag: $\$40$. 25 kg bag: $\$95$.
(a) Find the unit price per kg for each bag.
(b) Which size is the cheapest per kg?
(c) A family uses 30 kg per month. Find the cheapest monthly cost (you must buy whole bags). 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 Mia's dad says “always grab the biggest pack — it's always cheaper per kg”. In your own words, explain (i) why this rule is USUALLY true but NOT always, (ii) what specific calculation you should do at the shelf to check, (iii) give one realistic example (using your own made-up numbers) where the smaller pack wins, and (iv) give one realistic example where the biggest pack does win. Use the phrase “unit price” somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Cordial
(a) 2 L: $\$5.00 \div 2 = \textbf{\$2.50/L}$. 1.5 L: $\$3.60 \div 1.5 = \textbf{\$2.40/L}$.
(b) The 1.5 L bottle is the better buy ($\$0.10/L$ cheaper).
(c) No, Mia is wrong this time — the smaller 1.5 L bottle is actually cheaper per L. Always calculate; don't assume.
1.2 — Three brands of pasta
(a) A: $\$2.50 \div 0.5 = \textbf{\$5.00/kg}$. B: $\$4.80 \div 1 = \textbf{\$4.80/kg}$. C: $\$3.90 \div 0.75 = \textbf{\$5.20/kg}$.
(b) Cheapest → most expensive: B ($\$4.80$) < A ($\$5.00$) < C ($\$5.20$).
(c) With $\$10$, Brand B gives you the most pasta: $10 \div 4.80 \approx 2.08$ kg, vs A $\approx 2$ kg, vs C $\approx 1.92$ kg. Brand B gives the most (about 2.08 kg).
1.3 — Dishwashing liquid
(a) 750 mL: $\$5.25 \div 7.5 = \textbf{\$0.70/100 mL}$. 1.5 L = 1500 mL: $\$9.00 \div 15 = \textbf{\$0.60/100 mL}$.
(b) The 1.5 L bottle is cheaper per 100 mL.
(c) Saving = $\$0.70 - \$0.60 = \textbf{\$0.10/100 mL}$ (= $\$1.00/L$).
1.4 — Cereal
(a) 250 g: $\$4.00 \div 2.5 = \textbf{\$1.60/100 g}$. 400 g: $\$5.60 \div 4 = \textbf{\$1.40/100 g}$.
(b) The 400 g box is cheaper per 100 g.
(c) For 1 kg/week using 400 g boxes: $1000 \div 400 = 2.5$ boxes — round up to 3 boxes = 1.2 kg for $3 \times \$5.60 = \$16.80$/week. (If exactly 1 kg is needed and they don't mind mixing sizes: 2 of the 400 g + 1 of the 250 g (?) — but the cleanest answer is 3 × 400 g = $\$16.80$.)
1.5 — Bulk rice
(a) 5 kg: $\$22 \div 5 = \textbf{\$4.40/kg}$. 10 kg: $\$40 \div 10 = \textbf{\$4.00/kg}$. 25 kg: $\$95 \div 25 = \textbf{\$3.80/kg}$.
(b) 25 kg bag is cheapest per kg.
(c) For exactly 30 kg, cheapest combo of whole bags: 1 × 25 kg ($\$95$) + 1 × 5 kg ($\$22$) = $\$117$. (Compare: 3 × 10 kg = $\$120$; 6 × 5 kg = $\$132$. So $\$117$ wins.)
2.1 — Explain your thinking (sample response)
Dad's rule — “always grab the biggest pack” — is USUALLY true because supermarkets normally give a bulk discount, so the unit price (cost per kg, per L or per 100 g) tends to drop as pack size grows. But it's NOT always true, because the medium or small pack can be on special, or the “family size” can be priced for the convenience tax it carries. The check at the shelf is simple: calculate unit price = cost ÷ quantity, in the same unit for every option. A realistic example where the smaller pack wins: 1.5 L cordial for $\$3.60$ ($\$2.40/L$) beats a 2 L bottle for $\$5.00$ ($\$2.50/L$). A realistic example where the bigger pack wins: 25 kg of rice for $\$95$ ($\$3.80/kg$) easily beats a 5 kg bag at $\$22$ ($\$4.40/kg$). The lesson: don't assume — always do the unit-price calculation.
Marking: 1 mark for explaining “usually but not always” with a reason; 1 mark for naming the unit-price check (cost ÷ quantity); 1 mark for a realistic smaller-pack-wins example with the numbers; 1 mark for a realistic bigger-pack-wins example with the numbers.