Mathematics • Year 8 • Unit 1 • Lesson 14
Best Buy — Mixed Challenge
Pull together everything from Lesson 14: unit price calculation, picking sensible units, multi-option comparison, and the “bigger isn't always cheaper” trap. Six mixed problems, one “find the mistake”, and one open-ended challenge.
1. Mixed problems — choose the right move
Each question uses a different combination of ideas from Lesson 14. Decide which move applies before you start writing. Show your working. 3 marks each
1.1 600 g of jam for $\$5.40$. Find the unit price in $/100 g AND in $/kg.
1.2 250 mL of pure orange juice for $\$3.00$ vs 1 L for $\$10$. Which is cheaper per L?
1.3 A 200 g block of chocolate is $\$4$. A 350 g block is $\$6.30$. Find the unit price per 100 g for each and decide the better buy.
1.4 Compare Pack A: $\$3.20/L$ vs Pack B: $\$1.50/500 mL$. Which is cheaper per L? Show working.
1.5 Toilet paper rolls: 6-pack for $\$5.40$; 12-pack for $\$10$; 24-pack for $\$22$. Find the unit price per roll for each and rank them cheapest to most expensive.
1.6 Tina compares two coffee tins: 200 g for $\$8$ and 500 g for $\$22$. (a) Find the unit price per 100 g for each. (b) Which is the better buy? (c) For $\$50$, what is the largest amount (in g) of the better-buy coffee she could get with whole tins?
2. Find the mistake
Another student is trying to decide between two laundry powders. Their working is shown below. Exactly one line contains the key mistake. Spot it, explain why it's wrong, then re-do the comparison correctly. 3 marks
Student's working — which is cheaper per kg: $\$15$ for 2 kg, or $\$22$ for 3 kg?
Line 1: Pack A is 2 kg for $\$15$. Per kg: $\$15 \div 2 = \$7.50/$kg.
Line 2: Pack B is 3 kg for $\$22$. Per kg: $\$22 - \$3 = \$19$, then $\$19 \div 3 \approx \$6.33$/kg.
Line 3: $\$6.33 \lt \$7.50$.
Line 4: So Pack B is the better buy.
(a) Which line contains the key mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Re-do the working correctly. Does Pack B still win? Give the correct unit prices and conclusion.
Stuck? Unit price is just cost ÷ weight — no random subtraction step. Recalculate Pack B properly.3. Open-ended challenge — design a tricky shelf
This question has more than one valid answer. 4 marks
3.1 Design three pack sizes of the same product (e.g., pasta) where:
- the three packs have three different sizes (small, medium, large),
- the LARGEST pack is NOT the cheapest per kg, and
- each pack price is a sensible whole-dollar (or 50c) amount.
Write:
(i) Your three packs (size + price) in a small table.
(ii) The unit price ($/kg) for each.
(iii) The ranking from cheapest to most expensive per kg.
(iv) The “trap pack” that a careless shopper might pick (because it's the biggest) and the dollar amount they'd OVERSPEND per kg vs the best buy.
Bonus: In one line, explain why supermarkets are now required to print unit prices on shelf labels.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Jam
Per 100 g: $\$5.40 \div 6 = \textbf{\$0.90/100 g}$. Per kg: $\$5.40 \div 0.6 = \textbf{\$9.00/kg}$. (Same value, two units.)
1.2 — Orange juice
250 mL = 0.25 L: $\$3 \div 0.25 = \textbf{\$12/L}$. 1 L: $\textbf{\$10/L}$. The 1 L bottle is cheaper per L by $\$2$.
1.3 — Chocolate
200 g: $\$4 \div 2 = \textbf{\$2.00/100 g}$. 350 g: $\$6.30 \div 3.5 = \textbf{\$1.80/100 g}$. 350 g block is the better buy ($\$0.20/100$ g cheaper).
1.4 — Pack A vs Pack B
Pack A: $\$3.20/L$ given. Pack B: $\$1.50 \div 0.5 = \$3.00/L$. Pack B is cheaper per L by $\$0.20$.
1.5 — Toilet paper
6-pack: $\$5.40 \div 6 = \$0.90/$roll. 12-pack: $\$10 \div 12 \approx \$0.833/$roll. 24-pack: $\$22 \div 24 \approx \$0.917/$roll.
Cheapest → most expensive: 12-pack ($\$0.83$) < 6-pack ($\$0.90$) < 24-pack ($\$0.92$). The 24-pack is the most expensive per roll — classic trap!
1.6 — Coffee
(a) 200 g: $\$8 \div 2 = \textbf{\$4.00/100 g}$. 500 g: $\$22 \div 5 = \textbf{\$4.40/100 g}$.
(b) The 200 g tin is the better buy ($\$0.40/100$ g cheaper).
(c) With $\$50$ and 200 g tins at $\$8$: $50 \div 8 = 6.25$ → 6 whole tins = 1200 g for $\$48$, with $\$2$ change.
2 — Find the mistake
(a) The mistake is on Line 2.
(b) The student invented a “$\$22 - \$3$” step (perhaps reading the “3” from “3 kg” as something to subtract). Unit price is simply cost ÷ quantity — no subtraction.
(c) Corrected: Pack A $\$15 \div 2 = \textbf{\$7.50/kg}$ (same as student). Pack B $\$22 \div 3 \approx \textbf{\$7.33/kg}$. $\$7.33 \lt \$7.50$, so Pack B is still the better buy, but the saving is only about $\$0.17/$kg, not $\$1.17/$kg as the student's bogus working suggested.
3 — Open-ended challenge (sample solution)
(i) Three packs of pasta:
- Small: 250 g — $\$2.00$.
- Medium: 500 g — $\$3.50$.
- Large: 1 kg — $\$8.00$.
(ii) Unit prices: Small $\$2 \div 0.25 = \$8/$kg; Medium $\$3.50 \div 0.5 = \$7/$kg; Large $\$8/$kg.
(iii) Ranking cheapest to most expensive per kg: Medium ($\$7) < Small ($\$8) = Large ($\$8).
(iv) Trap pack: Large 1 kg — a shopper grabbing the biggest pack pays $\$8/$kg, which is $\$1/$kg MORE than the medium's $\$7/$kg. Over 1 kg, that's $\$1$ overspend per kg.
Bonus: Supermarkets must print unit prices so shoppers can compare different pack sizes (and different brands) on a fair, like-for-like basis without doing the maths in the aisle.
Marking: 1 mark for three sensible packs with different sizes; 1 mark for correct unit prices for all three; 1 mark for the ranking AND identifying the largest as not the best; 1 bonus mark for the “why labels exist” explanation.