Year 7 Maths Ratios, Rates and Time

Best Buys

Q: What is a unit price?

The price for one unit, such as $ per kg, per L, per item or per 100 g.

Q: How do you find the best buy?

Find the unit price of each item in the same units and choose the lowest.

Q: How do you find the price per 100 g?

Divide the price by the number of lots of 100 g. $4.80 for 250 g is 4.80 ÷ 2.5 = $1.92 per 100 g.

Q: Is the biggest pack always the best buy?

No. Always check the unit price of every size.

Q: How do you work out a saving?

Find the cost both ways and subtract.

20 practice questions 1 video lesson Theory + worked examples

The best buy is the item that gives you the most for your money, found by comparing unit prices. In NSW Year 7 maths this is a practical use of rates, such as dollars per kilogram or per 100 g (NESA outcome MA4‑RAT‑C‑01).

You will change every item to the same unit, divide price by quantity, round to the nearest cent, compare and write a clear conclusion, work out the saving between two options, and take off any discount first. Reading supermarket shelf labels and judging “3 for $6.60” deals use exactly these skills. This subtopic is part of Year 7 Ratios, Rates and Time.

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Theory

The best buy is the item with the lowest unit price: the price for one item, or for the same amount, such as per kilogram, per litre or per $100$ grams. This Year 7 maths page shows how to find and compare unit prices, and how to work out savings, discounts and specials.

A unit price is a rate in dollars per unit, such as $\$$ per kg or $\$$ per L: unit price $=$ price $\div$ quantity.

Step 1. Use the same unit for every item: change kg to g or mL to L first ($1.2$ kg $= 1200$ g).
Step 2. Find each unit price. For a price per $100$ g, count the lots of $100$ g: $250$ g is $2.5$ lots, so divide the price by $2.5$. Round to the nearest cent.
Step 3. Compare and write a sentence: “$\$0.60 < \$0.70$, so the $1$ kg tub is the better buy.”

Another way: find how much one dollar buys. The item that gives more for $\$1$ is the better buy.

A saving is a difference: the cost one way minus the cost the other way. Discounts first: take off any discount before finding the unit price ($20\%$ off $\$15$ is $15 \times 0.8 = \$12$).

Supermarket shelf labels show the unit price under the price. $\$3.50$ is less than $\$6.00$, but the $1$ kg tub costs less for each $100$ g, so it is the better buy.

The rule:

\[ \text{unit price} = \text{price} \div \text{quantity} \]

unit price = price \div quantity

\[ \text{price per 100 g} = \text{price} \div (\text{grams} \div 100) \]

price per 100 g = price \div (grams \div 100)

          The lower price is not always the better buy. Compare the unit prices, not the prices of different sizes.
        

          A bigger pack is not always cheaper. Work out the unit price of every size before you decide.
        

          Going backwards. Price \(=\) unit price \(\times\) quantity. At \(\$0.80\) per \(100\) g, a \(350\) g bag costs \(0.80 \times 3.5 = \$2.80\).
        

How to find the best buy

Change every item to the same unit.
Take off any discount or work out any special first.
Divide each price by its quantity (or by the lots of $100$ g).
Compare the unit prices: the lowest is the best buy. Write a sentence.

Example 1 — Price per item

A carton of $12$ eggs costs $\$6.50$. A tray of $30$ eggs costs $\$15.90$. Which is the better buy?

Solution

$6.50 \div 12$	$=$	$0.5416\ldots$
$15.90 \div 30$	$=$	$0.53$

6.50 \div 12 \approx 0.54, 15.90 \div 30 = 0.53

$\$0.53 < \$0.54$ per egg, so the tray of $30$ is the better buy.

Example 2 — Price per gram

Which is the better buy: $70$ g of cooking chocolate for $\$5.60$, or $1.5$ kg for $\$90$?

Solution

$5.60 \div 70$	$=$	$0.08$
$1.5 \times 1000$	$=$	$1500$
$90 \div 1500$	$=$	$0.06$

5.60 \div 70 = 0.08 per g 1.5 kg = 1500 g, 90 \div 1500 = 0.06 per g

$\$0.06 < \$0.08$ per gram, so $1.5$ kg for $\$90$ is the better buy.

Example 3 — What does one dollar buy?

Which is the better buy: a $48$ g packet of chips for $\$1.20$, or a $100$ g packet for $\$2.00$?

Solution

$48 \div 1.20$	$=$	$40$
$100 \div 2$	$=$	$50$

48 \div 1.20 = 40 g per dollar, 100 \div 2 = 50 g per dollar

$\$1$ buys $40$ g of the small packet but $50$ g of the big packet, so the $100$ g packet is the better buy.

Example 4 — Price per 100 grams

Cheese costs $\$4.80$ for a $250$ g block or $\$17.50$ for a $1$ kg block. Which is the better buy?

Solution

$4.80 \div 2.5$	$=$	$1.92$
$17.50 \div 10$	$=$	$1.75$

4.80 \div 2.5 = 1.92 per 100 g, 17.50 \div 10 = 1.75 per 100 g

$\$1.75 < \$1.92$ per $100$ g, so the $1$ kg block is the better buy.

Example 5 — Bigger is not always cheaper

Flour is sold as $1$ kg for $\$2.20$, $2$ kg for $\$4.00$ and $5$ kg for $\$11.50$.
(i) Which bag is the best buy?
(ii) How much is saved on $10$ kg by buying the best bags instead of $1$ kg bags?

Solution

$4.00 \div 2$	$=$	$2$
$11.50 \div 5$	$=$	$2.3$
$10 \times 2.20 - 5 \times 4.00$	$=$	$2$

per kg 2.20, 2.00, 2.30 22.00 - 20.00 = 2.00

(i) The $2$ kg bag ($\$2.00$/kg, less than $\$2.20$ and $\$2.30$)
(ii) $\$2.00$

Example 6 — A multi-buy special

Brand A juice is $\$5.80$ for $2$ L, but this week it is “$2$ bottles for $\$9.00$”. Brand B is $\$7.50$ for $3$ L.
(i) Find each price per litre with the special.
(ii) How much is saved on $12$ L by buying the better buy?

Solution

$9.00 \div 4$	$=$	$2.25$
$7.50 \div 3$	$=$	$2.5$
$4 \times 7.50 - 3 \times 9.00$	$=$	$3$

A 9.00 \div 4 = 2.25 per L, B 7.50 \div 3 = 2.50 per L 30.00 - 27.00 = 3.00

(i) A $\$2.25$/L, B $\$2.50$/L, so Brand A is the better buy.
(ii) $12$ L is $3$ Brand A deals or $4$ bottles of Brand B: $\$30.00 - \$27.00 = \$3.00$ saved.

Common pitfalls

Comparing prices, not unit prices. A cheaper packet may be a smaller amount.

Different units. Change $600$ mL to $0.6$ L (or $2$ L to $2000$ mL) before dividing.

Rounding too early. Round each unit price to the nearest cent only at the end.

Forgetting the discount. Find the sale price first, then the unit price.

Frequently asked questions

What is a unit price?

The price for one unit, such as $\$$ per kg, per L, per item or per $100$ g.

How do you find the best buy?

Find the unit price of each item in the same units and choose the lowest.

How do you find the price per 100 g?

Divide the price by the number of lots of $100$ g. $\$4.80$ for $250$ g is $4.80 \div 2.5 = \$1.92$ per $100$ g.

Is the biggest pack always the best buy?

No. Always check the unit price of every size.

How do you work out a saving?

Find the cost both ways and subtract.

\(6.50 \div 12\)	\(=\)	\(0.5416\ldots\)
\(15.90 \div 30\)	\(=\)	\(0.53\)

\(5.60 \div 70\)	\(=\)	\(0.08\)
\(1.5 \times 1000\)	\(=\)	\(1500\)
\(90 \div 1500\)	\(=\)	\(0.06\)

\(48 \div 1.20\)	\(=\)	\(40\)
\(100 \div 2\)	\(=\)	\(50\)

\(4.80 \div 2.5\)	\(=\)	\(1.92\)
\(17.50 \div 10\)	\(=\)	\(1.75\)

\(4.00 \div 2\)	\(=\)	\(2\)
\(11.50 \div 5\)	\(=\)	\(2.3\)
\(10 \times 2.20 - 5 \times 4.00\)	\(=\)	\(2\)

\(9.00 \div 4\)	\(=\)	\(2.25\)
\(7.50 \div 3\)	\(=\)	\(2.5\)
\(4 \times 7.50 - 3 \times 9.00\)	\(=\)	\(3\)

Best Buys

📖 Theory

How to find the best buy

Common pitfalls

Frequently asked questions

Theory