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GCSE Maths Ratio and Proportion

Best Buy

Best Buy Maths

Q: Note the cost of the items and the number of items for each deal.

In this example we are told that [katex] 2kg [/katex] of pasta [katex] = £4.40 [/katex] and [katex] 1.5kg [/katex] of pasta [katex] = £3.60. [/katex]

Q: Compare the prices of the equivalent quantities.

Offer A is better value as [katex] £2.20 [/katex] per kilogram of pasta is cheaper than [katex] £2.40 [/katex] per kilogram of pasta. Alternatively we could work out how much pasta can be bought for [katex] £1. [/katex] Here we can see that Offer A gives us more pasta per [katex] £, [/katex] so is better value.

Q: Note the cost of the items and the number of items for each deal.

In this example we are told that [katex] 3 [/katex] t-shirts [katex] =£14 [/katex] and [katex] 4 [/katex] t-shirts [katex] =£18. [/katex]

Q: Note the cost of the items and the number of items for each deal.

Here we are told that [katex] 200ml=£0.80, \ 500ml=£1.80 [/katex] and [katex] 1l, [/katex] or [katex] 1000ml=£3.50. [/katex]

Q: Compare the prices of the equivalent quantities.

Offer C is the best value since [katex] £3.50 [/katex] is the lowest cost for [katex] 1000ml [/katex] of cola.

Here we will learn about best buy maths, including the unitary method, common multiples (including LCM), exchange rates and shopping deals.

There are also best buy maths worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is best buy maths?

Best buys problems involve assessing which item is the best value for money.

To do this we could use the following methods,

Unitary method – this involves calculating the price per unit for each item.

Common multiples – here we find a common multiple of the number of units we have and use this make comparisons.

Shop deals – we interpret deals such as ‘ $3$ for $2$ ’, ‘buy one get one free’ or a percentage extra free.

Exchange rates – if the prices are in different currencies, we convert them to the same currency to compare them.

In a question you may be asked which of $2$ or more products is the better value. This would indicate that you are being asked to find which of the products is the best buy.

Best buy problems may also be known as cost problems. We have to compare the cost of $2$ or more items and then decide which of the items is the best value.

What is best buy?

How to use best buy maths

In order to compare deals:

Note the cost of the items and the number of items for each deal.
Calculate the price for an equivalent number of items for each deal.
For the unitary method, this is the price of a single item. For the common multiples method, this is the price of a common number of items.
Compare the prices of the equivalent quantities.

In order to use exchange rates:

Identify the exchange rate and currency to be converted.
Convert the currency.
Compare the values in the same currency to identify the best value.

Explain how to use best buy maths

Best buy maths worksheet

Get your free best buy maths worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Best buy maths worksheet

Get your free best buy maths worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Best buy maths examples

Example 1: unitary method

Offer A	Offer B
$3$ footballs	$7$ footballs
$£12$	$£35$

Note the cost of the items and the number of items for each deal.

In this example, we are told that $3$ footballs $= £12$ and $7$ footballs $= £35.$

2Calculate the price for an equivalent number of items for each deal.

For the unitary method, this is the price of a single item. For the common multiples method, this is the price of a common number of items.

In this example we are going to use the unitary method, calculating the price of 1 football for each deal.

3Compare the prices of the equivalent quantities.

Offer A is better value as $£4$ per football is cheaper than $£5$ per football.

Step-by-step guide: Unitary method (coming soon)

Example 2: unitary method

Offer A	Offer A
$2kg$ of pasta	$1.5kg$ of pasta
$£4.40$	$£3.60$

Note the cost of the items and the number of items for each deal.

In this example we are told that $2kg$ of pasta $= £4.40$ and $1.5kg$ of pasta $= £3.60.$

Calculate the price for an equivalent number of items for each deal.

For the unitary method, this is the price of a single item. For the common multiples method, this is the price of a common number of items.

We are going to use the unitary method and calculate the price of $1kg$ of pasta for each deal.

Compare the prices of the equivalent quantities.

Offer A is better value as $£2.20$ per kilogram of pasta is cheaper than $£2.40$ per kilogram of pasta.

Alternatively we could work out how much pasta can be bought for $£1.$

Here we can see that Offer A gives us more pasta per $£,$ so is better value.

Example 3: common multiples

Offer A	Offer A
$3$ t-shirts	$4$ t-shirts
$£14$	$£18$

Note the cost of the items and the number of items for each deal.

In this example we are told that $3$ t-shirts $=£14$ and $4$ t-shirts $=£18.$

Calculate the price for an equivalent number of items for each deal.

For the unitary method, this is the price of a single item. For the common multiples method, this is the price of a common number of items.

This time we are going to use common multiples. This method is useful when the total prices are not easily divisible by the number of items.

$12$ is a common multiple of $3$ and $4$ so we are going to find the price of $12$ t-shirts using each offer.

Compare the prices of the equivalent quantities.

Offer B is better value since the same number of t-shirts would cost less using this offer.

Example 4: common multiples

Offer A	Offer B	Offer C
$200ml$ cola	$500ml$ cola	$1l$ cola
$£0.80$	$£1.80$	$£3.50$

Note the cost of the items and the number of items for each deal.

Here we are told that $200ml=£0.80, \ 500ml=£1.80$ and $1l,$ or $1000ml=£3.50.$

Calculate the price for an equivalent number of items for each deal.

For the unitary method, this is the price of a single item. For the common multiples method, this is the price of a common number of items.

The easiest method to use here is the common multiples method.

$1000$ is a common multiple of $200, 500$ and $1000$ so we are going to find the price of $1000ml$ for each offer.

Compare the prices of the equivalent quantities.

Offer C is the best value since $£3.50$ is the lowest cost for $1000ml$ of cola.

Example 5: deals

A shop is selling the same jumper on two different offers.

Which offer is better value for money?

Offer A	Offer B
Buy one get one free	$3$ for $2$
Jumpers cost $£20$	Jumpers cost $£18$ each

Note the cost of the items and the number of items for each deal.

For this question we need to think more carefully.

For Offer A, which is buy one get one free, we will get $2$ jumpers for $£20.$

For Offer B, which is $3$ for $2,$ we will get $3$ jumpers for $£18 \times 2=£36.$

Calculate the price for an equivalent number of items for each deal.

For the unitary method, this is the price of a single item. For the common multiples method, this is the price of a common number of items.

Applying the unitary method we can calculate the price of one jumper for each offer.

Compare the prices of the equivalent quantities.

Offer A is better since the cost of each jumper is less.

Example 6: deals

A shop is selling the same chocolate bars on two different offers.

Which offer is better value for money?

Offer A	Offer B
$20\%$ off the price	$50\%$ extra free
$250g$ bar costs $£5$	$120g$ bar costs $£3$

Calculate the total cost of the items and the total number of items for each deal.

For Offer A, we need to reduce the price by $20\%.$

$20\%$ of $£5= £1$

$£5-£1=£4$

The price of a $250g$ bar is $£4.$

For Offer B, we need to increase the weight of the bar by $50\%.$

$50\%$ of $120g=60g$

$120g+60g=180g$

The price for a $180g$ bar is $£3.$

Calculate the price for an equivalent number of items for each deal.

For the unitary method, this is the price of a single item. For the common multiples method, this is the price of a common number of items.

We are going to calculate the price of $1g$ of chocolate for each deal.

Compare the prices of the equivalent quantities.

Offer A is better since $1g$ of chocolate costs less using Offer A.

Example 7: exchange rates

The exchange rate is $£1 = \$1.50.$

A pair of trainers cost $£60$ in the UK.

The same pair of trainers cost $\$100$ in the USA.

Where is it cheaper to buy the trainers?

Identify the exchange rate and currency to be converted.

The exchange rate is $£1 = \$1.50.$

We need to convert $£60$ to $\$$ so that the currencies are the same and we can compare the amounts.

Convert the currency.

Converting $£60$ to $\$: £60 \times 1.50 = \$90$

Compare the values in the same currency to identify the best value.

The trainers cost $\$90$ in the UK.

The trainers cost $\$100$ in the USA.

They are cheaper in the UK.

Step-by-step guide: Exchange rates (coming soon)

Example 8: exchange rates

The exchange rates are $£1 = \$1.40$ and $£1 = €1.30.$

A game costs $£30$ in the UK.

The same game costs $\$49$ in the USA and $€32.50$ in France.

Where is it cheapest to buy the game?

Identify the exchange rate and currency to be converted.

The exchange rates are $£1 = \$1.40$ and $£1 = €1.30.$

Since both of the exchange rates involve $£,$ we are going to convert all of the prices to $£.$

Convert the currency.

Convert $\$49$ and $€32.50$ to $£$ .

$\$49 \div 1.40 = £35$

$€32.50 \div 1.30 = £25$

Compare the values in the same currency to identify the best value.

The game costs $£30$ in the UK, $£35$ in the USA and $£25$ in France.

It is the cheapest in France.

Common misconceptions

Understanding your calculation

For example, if $10$ tennis balls cost $£5,$ the price per ball would be $£5 \div 10=£0.50.$

An alternative would be to calculate $10 \div 5=2$ which is actually the number of balls for $£1.$ Each method is correct as long as it is comparable to the other offer and you compare them correctly.

Incorrect use of the exchange rate when converting currencies

If $£1= \$1.30,$ to convert $£$ to $\$$ we need to multiply by $1.30.$ To convert $\$$ to $£$ we need to divide by $1.30.$

Adding and subtracting amounts rather than using a multiplier

As you need to maintain proportion of amounts you should only multiply or divide to compare equivalence of amounts or values. Adding and subtracting does not maintain proportion.

Practice best buy maths questions

Offer A: each melon is $£3.$
Offer B: each melon is $£2.$
Offer B is better value for money.

Offer A: each melon is $£3.$
Offer B: each melon is $£2.$
Offer A is better value for money.

Offer A: each melon is $£15.$
Offer B: each melon is $£16.$
Offer A is better value for money.

Offer A: each melon is $£2.$
Offer B: each melon is $£3.$
Offer A is better value for money.

Offer A, $15 \div 5 = £3$ per melon.

Offer B, $16 \div 8 = £2$ per melon.

So Offer B is better value for money.

Offer A: $1 \ ml$ is $5p.$
Offer B: $1 \ ml$ is $4p.$
Offer A is better value for money.

Offer A: $1 \ ml$ is $0.5p$
Offer B: $1 \ ml$ is $0.4p.$
Offer B is better value for money.

Offer A: $1 \ ml$ is $£5.$
Offer B: $1 \ ml$ is $£4.$
Offer B is better value for money.

Offer A: $1 \ ml$ is $£0.50.$
Offer B: $1 \ ml$ is $£0.40$
Offer B is better value for money.

Write the prices in pence.

Offer A, $125 \div 250 = 0.5$ so $0.5$ pence per $ml.$

Offer B, $160 \div 400 = 0.4$ so $0.4$ pence per $ml.$

So Offer B is better value for money.

Offer A: $1$ pizza for $£9.$
Offer B: $1$ pizza for $£7.$
Offer C: $1$ pizza for $£8.$
So Offer B is the best value for money.

Offer A: $1$ pizza for $£7.$
Offer B: $1$ pizza for $£8.$
Offer C: $1$ pizza for $£9.$
So Offer A is the best value for money.

Offer A: $1$ pizza for $£8.$
Offer B: $1$ pizza for $£7.$
Offer C: $1$ pizza for $£9.$
So Offer C is the best value for money.

Offer A: $1$ pizza for $£8.$
Offer B: $1$ pizza for $£7.$
Offer C: $1$ pizza for $£9.$
So Offer B is the best value for money.

Offer A, $24 \div 3 = 8$ so $£8$ per pizza.

Offer B, $35 \div 5 = 7$ so $£7$ per pizza.

Offer C, $135 \div 15 = 9$ so $£9$ per pizza.

So Offer B is the best value for money.

Offer A is $£3.20$ per pen and Offer B is $£2.25$ per pen so Offer B is better value for money.

Offer A is $£1.60$ per pen and Offer B is $£1.50$ per pen so Offer B is better value for money.

Offer A is $£6.40$ per pen and Offer B is $£4.50$ per pen so Offer B is better value for money.

Offer A is $£6.40$ per pen and Offer B is $£6.75$ per pen so Offer A is better value for money.

Offer A is a total of $£3.20$ for two pens which means that each pen costs $£1.60.$

Offer B is a total of $£4.50$ for three pens which means that each pen is $£1.50.$

Therefore Offer B is better value for money.

Offer A is $50p$ per $100g$ and Offer B is $64p$ per $100g$ so Offer A is better value for money.

Offer A is $£1.80$ per $250g$ and Offer B is $£1.60$ per $250g$ so Offer B is better value for money.

Offer A is $£2$ per $100g$ and Offer B is $£1.56$ per $100g$ so Offer B is better value for money.

Offer A is $180g$ per $£1$ and Offer B is $125g$ per $£1$ so Offer B is better value for money.

Offer A: $10\%$ of $£2 = £0.20$
$£2-£0.20=£1.80$ so $360g$ for $£1.80.$
$£1.80 \div 3.6 =£0.50$ so $50p$ per $100g.$

Offer B: $25\%$ of $200g = 50g$
$200g + 50g = 250g$ so $250g$ for $£1.60.$
$£1.60 \div 2.5 =£0.64$ so $64p$ per $100g.$

UK: $£40$
USA: $45 \times 1.20 = £54$
The jumper is cheaper in the UK.

UK: $40 \times 1.20=\$48$
USA: $\$45$
The jumper is cheaper in the USA.

UK: $40 \div 1.20=\$33.33$
USA: $\$45$
The jumper is cheaper in the UK.

UK: $40 \times 1.20=\$48$
USA: $45 \div 1.20=£37.50$
The jumper is cheaper in the USA.

The exchange rate is $£1 = \$1.20$ so you need to multiply the price in pounds by $1.20.$

UK: $40 \times 1.20=\$48$

Best buy maths GCSE questions

1. Packs of pens are sold in two sizes.

$12$ pens cost $£3$
$20$ pens cost $£4$

Which size pack is better value for money?

You must show your working.

(3 marks)

Show answer

$12$ pack, $1$ pen is $25p$ .

(1)

$20$ pack, $1$ pen is $20p$ .

(1)

$20$ pack is better value for money.

(1)

2. (a) A shop is selling pictures.

A $10cm$ by $15cm$ picture costs $£45.$

An enlargement of the same picture is for sale.

The enlargement measures $12cm$ by $18cm$ and costs $£86.40.$

Which picture is better value for money?

(b) Why might you choose the picture that is not the best value for money?

(5 marks)

Show answer

(a)

Calculate area of a picture,

10 \times 15=150cm^2

$12 \times 18=216cm^2$ .

(1)

Calculates price of equivalent unit, for example price per square centimetre,

$£45 \div 150=£0.30$ per square centimetre

$£86.40 \div 216 =£0.40$ per square centimetre.

(1)

Calculates both equivalent values correctly.

$£0.30$ per square centimetre

and

$£0.40$ per square centimetre.

(1)

The smaller picture is better value for money as it costs $30p$ per square centimetre.

(1)

(b)

You might want a larger picture.

(1)

3. Michael wants to exchange some money from pounds to Euros. Two shops are offering different exchange rates. These are represented in the graph below.

best buy maths gcse question 3

The green dotted line represents Your Money and the blue solid line represents Cash for Travellers.

(a) Which shop has a better exchange rate and how do you know from looking at the graph?

(b) What are the exchange rates that each shop is offering?

(4 marks)

Show answer

(a)

Identifies that Your Money has the better exchange rate.

(1)

Identifies that Your Money has a steeper gradient.

(1)

(b)

Your Money, $£1 = €1.30$ .
Cash for travellers, $£1 = €1.10$ .

Calculates the gradient of one line.

(1)

Calculates the gradient of the second line.

(1)

Learning checklist

You have now learned how to:

Calculate value for money using a unitary method

Calculate value for money using common multiples and common factors

Calculate value for money with deals such as buy one get one free and

3

for the price of

2

Use exchange rates to convert money to different currencies

The next lessons are

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Introduction

What is best buy maths?

How to use best buy maths

Best buy maths worksheets

Best buy maths examples

↓

Example 1: unitary method Example 2: unitary method Example 3: common multiples Example 4: common multiples Example 5: deals Example 6: deals Example 7: exchange rates Example 8: exchange rates

Common misconceptions

Practice best buy maths questions

Best buy maths GCSE questions

Learning checklist

Next lessons

Still stuck

Offer A	Offer B	Offer C
3 pizzas	5 pizzas	15 pizzas
£24	£35	£135

Offer A	Offer B
10% off the price	25% extra free
360g bar costs £2	200g bar costs £1.60 each

Offer A	Offer B
5 melons	8 melons
£15	£16

Offer A	Offer B
250 ml of shampoo	400ml of shampoo
£1.25	£1.60