Mathematics • Year 8 • Unit 1 • Lesson 14
Best Buy, Unit Prices
Build fluency with unit prices: $/kg, $/100 g, $/L. One fully-worked example, one guided example with blanks, then eight independent problems from quick conversions to comparing two products fairly.
1. I do, fully worked example
Read every line. Each step has a short reason so you can see why bigger isn't always cheaper per kg.
Problem. 500 g of pasta costs $\$1.80$. A 1 kg bag of the same brand costs $\$3.20$. Which is the better buy?
Step 1, Pick a sensible unit for the comparison.
Both packs are in the kg range, compare per kg.
Reason: when sizes are similar in scale, per kg gives clean numbers.
Step 2, Unit price of the 500 g pack.
$500\ \text{g} = 0.5\ \text{kg}$; $\$1.80 \div 0.5 = \$3.60$/kg
Reason: convert grams to kg first so both unit prices use the same unit.
Step 3, Unit price of the 1 kg bag.
$\$3.20 \div 1 = \$3.20$/kg
Reason: the cost ÷ weight gives the per-kg price.
Step 4, Compare and decide.
$\$3.20 / \text{kg} < \$3.60 / \text{kg}$
Reason: the lower unit price is the cheaper-per-amount option, the better buy.
Answer: The 1 kg bag is the better buy ($\$0.40$/kg cheaper).
2. We do, fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Cereal Brand A: 250 g box for $\$4.00$. Brand B: 400 g box for $\$5.60$. Which is cheaper per 100 g?
Step 1, Pick a sensible unit. Both boxes are smaller than 1 kg, use per ________ g.
Step 2, Unit price of Brand A (250 g for $\$4.00$):
$\$4.00 \div $ ______ (number of 100 g lots) $= \$$ ______ / 100 g
Step 3, Unit price of Brand B (400 g for $\$5.60$):
$\$5.60 \div $ ______ (number of 100 g lots) $= \$$ ______ / 100 g
Step 4, Compare:
$\$$ ______ < $\$$ ______, so Brand ______ is cheaper per 100 g.
3. You do, independent practice
Show your working in the space under each problem. The first four are foundation (single unit-price calculation). The middle two are standard (compare two products in the same units). The last two are extension (mixed units, or three-way comparison).
Foundation, find one unit price
3.1 A 400 g pack of chips costs $\$4.00$. Find the price per 100 g. 1 mark
3.2 500 g of bananas at $\$2.50$. Find the price per kg. 1 mark
3.3 1.2 kg of rice for $\$4.80$. Find the price per 100 g. 1 mark
3.4 $\$6$ for 750 g of cheese. Find the price per kg. 1 mark
Standard, compare two products in the same units
3.5 Juice: 2 L bottle for $\$6.40$, or 1.5 L bottle for $\$5.10$. Find the unit price per L for each, and decide which is the better buy. 2 marks
3.6 Laundry powder: $\$15$ for 2 kg, or $\$22$ for 3 kg. Find the unit price per kg for each, and decide which is cheaper per kg. 2 marks
Extension, mixed units, or three-way comparison
3.7 Brand A is $\$2.10$ for 500 g; Brand B is $\$3.50$/kg. Which is cheaper per kg? Convert both to $/kg before comparing. 2 marks
3.8 Three cereal boxes: A: 250 g for $\$3.50$; B: 500 g for $\$6$; C: 1 kg for $\$13.50$. (a) Find the unit price per kg for each. (b) Rank them cheapest to most expensive per kg. (c) Which one is “bigger but NOT cheaper”? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do (cereal A vs B per 100 g)
Step 1: per 100 g.
Step 2: $\$4.00 \div \textbf{2.5} = \textbf{\$1.60}/100$ g.
Step 3: $\$5.60 \div \textbf{4} = \textbf{\$1.40}/100$ g.
Step 4: $\$\textbf{1.40} \lt \$\textbf{1.60}$, so Brand B is cheaper per 100 g.
3.1, Chips
$\$4.00 \div 4 = \textbf{\$1.00}/100$ g (400 g = 4 lots of 100 g).
3.2, Bananas
500 g = 0.5 kg. $\$2.50 \div 0.5 = \textbf{\$5.00}/$kg.
3.3, Rice
1.2 kg = 12 lots of 100 g. $\$4.80 \div 12 = \textbf{\$0.40}/100$ g.
3.4, Cheese
750 g = 0.75 kg. $\$6 \div 0.75 = \textbf{\$8.00}/$kg.
3.5, Juice
2 L for $\$6.40$: $\$6.40 \div 2 = \$3.20/$L. 1.5 L for $\$5.10$: $\$5.10 \div 1.5 = \$3.40/$L. The 2 L bottle is the better buy ($\$0.20$/L cheaper).
3.6, Laundry powder
2 kg for $\$15$: $\$15 \div 2 = \$7.50/$kg. 3 kg for $\$22$: $\$22 \div 3 \approx \$7.33/$kg. The 3 kg pack is cheaper per kg (by about $\$0.17/$kg).
3.7, Brand A vs Brand B
Brand A: $\$2.10 \div 0.5 = \$4.20/$kg. Brand B: $\$3.50/$kg (given). $\$3.50 \lt \$4.20$, so Brand B is cheaper per kg by $\$0.70/$kg.
3.8, Three cereal boxes
(a) A: $\$3.50 \div 0.25 = \$14/$kg. B: $\$6 \div 0.5 = \$12/$kg. C: $\$13.50/$kg.
(b) Cheapest → most expensive per kg: B ($\$12$) < C ($\$13.50$) < A ($\$14$).
(c) Box C is “bigger but NOT cheaper”, it's the largest pack (1 kg) but Brand B's 500 g box beats it per kg.