# Find the Best Value for Money

In this worksheet, students will find the costs of single units within larger packs, so that they can compare prices and decide which options represents the best value purchase.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Calculations with Ratio

Difficulty level:

### QUESTION 1 of 10

Being able to make best value choices is all about comparing the value of two objects to idnetify which represents the best value - an important skill in maths but also in life too!

You will have been to a supermarket and seen the different sizes of products, which are all priced differently too.

The question is, which one should you buy which represents the best value?

The key to solving problems of this type is to find the cost of one of the objects or one of the units of measurements

Let's look at this in action now using an example.

e.g. A pack of 4 toilet rolls cost £2.16 and a pack of 9 costs £4.77. Which pack is better value?

Firstly, we need to find the cost of 1 roll in each pack:

4 rolls cost 216 p so 1 roll costs 54 p (216 ÷ 4)

9 rolls cost 477 p so 1 roll costs 53 p (477 ÷ 9)

The cost of a single roll in the pack of four is 54 p, whilst a roll in the 9-pack costs 53 p

So the 9-pack roll represents the best value, as each roll costs slightly less in this pack.

You may think that this is often the case, and that larger packs usually represent better value.

However, this is not always true

For example, a smaller pack may be on special offer (which reduces the price of each unit) whilst the larger pack is not.

So be careful to not jump to conclusions, and always calculate before you make any decisions.

In this activity, we will find the costs of single units within larger packs so that we can compare prices and decide which options represents the best value purchase.

Type a word in the space to complete the sentence below.

12 doughnut costs £4 and a pack of 32 costs £10.

Which option represents the best value?

12 pack

32 pack

50 kg of coal costs £12.

75 kg costs £17.

Which option represents the best value?

50 kg

75 kg

I am trying to find out which is better value - a 3 litre or a 6 litre bottle of orange juice.

Which size should I find out the cost of, in order to compare these two amounts?

If you think that there is more than one option here, then please only record one number in the box below, or you may be marked incorrectly.

50 kg

75 kg

Anna and Andy are comparing their running times.

Anna ran 10 miles in 62 minutes.

Andy ran 10 km in 40 minutes.

Who is the faster runner?

You should use the conversion 5 miles = 8 km in this question.

Andy

Anna

For each situation outlined below, select if the first or second option presented represents the best value.

A small tin (350 g) of coffee costs £2.70.

A medium tin (500 g) costs £3.90.

A large tin (700 g) costs £5.40.

Which of these options represent the best value?

Small

Medium

Large

Imagine a friend is working on the problem below.

500 ml of water costs £1.

350 ml of water costs 72 p.

Which of these options is the best value?

They have created the lines of working shown below to find their answer.

Mark each line of their working as either 'Correct' or 'Incorrect'.

A small container (150 g) of washing powder costs £1.59.

A medium container (250 g) costs £2.65.

A large container (350 g) costs £3.85.

Which of these options represent the best value?

Small

Medium

Large

1 doughnut costs 40 p and a pack of 3 costs £1.23.

Which option represents the best value?

1 doughnut

Pack of 3 doughnuts

• Question 1

Type a word in the space to complete the sentence below.

EDDIE SAYS
To be able to compare, we need to find the same amount of each. Usually, we choose to find the amount linked to a single unit, as this creates the easiest calculations to work with. However, we can actually choose to find any amount that we wish, so long as we find exactly the same amount of each.
• Question 2

12 doughnut costs £4 and a pack of 32 costs £10.

Which option represents the best value?

32 pack
EDDIE SAYS
12 doughnuts cost 400 p, so 1 doughnut costs 33 p (400÷ 12, rounded to the nearest p) 32 doughnuts cost 1000 p, so 1 doughnut costs 31 p (1000 ÷ 32, rounded to the nearest p) Which option represents better value, 33 p or 31 p? The 32-pack represents the best value, as a doughnut in this pack costs slightly less than it does in the 12-pack.
• Question 3

50 kg of coal costs £12.

75 kg costs £17.

Which option represents the best value?

75 kg
EDDIE SAYS
50 kg of coal costs £12 (1200 p), so 1 kg costs 24 p (1200÷ 50) 75 kg of coal costs £17 (1700 p), so 1 kg costs 23 p (1700÷ 75 rounded to the nearest p) Which option represents better value, 24 p or 23 p? The 75 kg sack represents the best value, as a kilogram in this sack costs slightly less than it does in the 50 kg sack.
• Question 4

I am trying to find out which is better value - a 3 litre or a 6 litre bottle of orange juice.

Which size should I find out the cost of, in order to compare these two amounts?

If you think that there is more than one option here, then please only record one number in the box below, or you may be marked incorrectly.

EDDIE SAYS
There are a few different choices here, but three that are the most sensible choices. We could find out the cost of 1 litre of each bottle. We could find out the cost of 3 litres of each. This means we only have to halve the cost of the 6 litre bottle, which is an easier calculation. We could find out the cost of 6 litres of each. This means we only have to double the cost of the 3 litre bottle, which is also easier. Which of these options did you choose?
• Question 5

Anna and Andy are comparing their running times.

Anna ran 10 miles in 62 minutes.

Andy ran 10 km in 40 minutes.

Who is the faster runner?

You should use the conversion 5 miles = 8 km in this question.

Anna
EDDIE SAYS
The first thing we need to do here is to change the values so that they are expressed in the same units. Anna ran 10 miles. Using the conversion factor we have been given, we can find that this is the same as 16 km (10 ÷ 5 × 8). We can now rewrite the question as: Anna ran 16 km in 62 minutes. Andy ran 10 km in 40 minutes. If we now find the time taken to run 1 km by each person, we can compare them directly. Anna runs 1 km in 3.9 mins (62 ÷ 16). Andy runs 1 km in 4 mins (40 ÷ 10). So Anna runs slightly faster than Andy.
• Question 6

For each situation outlined below, select if the first or second option presented represents the best value.

EDDIE SAYS
Don't make the common mistake of assuming that the larger option is always better value! In the first scenario, we can see that the first option is actually more expensive than the second one, as 100 g costs £1 or 100 g costs 90 p. In the second scenario, 100 g costs £1.33 or 100 g costs £1.50. Did you mark the correct options in the grid to show whether the first or second amount represented better value?
• Question 7

A small tin (350 g) of coffee costs £2.70.

A medium tin (500 g) costs £3.90.

A large tin (700 g) costs £5.40.

Which of these options represent the best value?

Small
Large
EDDIE SAYS
All of these weights can be changed easily to 50 g so that they can be compared. (Although you could easily change them all to 1 g if you prefer.) Small: 38.6 p per 50 g (270 ÷ 7) Medium: 39 p per 50 g (390 ÷ 10) Large: 38.6 p per 50 g (540 ÷ 14) So the best value is actually either the large or small jar, as they both cost exactly the same per 50 g.
• Question 8

Imagine a friend is working on the problem below.

500 ml of water costs £1.

350 ml of water costs 72 p.

Which of these options is the best value?

They have created the lines of working shown below to find their answer.

Mark each line of their working as either 'Correct' or 'Incorrect'.

EDDIE SAYS
Beware of this error and never round too much during your working! The cost of 50 ml in the small bottle is actually 10.29 p (72 ÷ 7). So it actually represents very slightly worse value than the large bottle option. This means that the final two lines of working are incorrect. Did you spot that?
• Question 9

A small container (150 g) of washing powder costs £1.59.

A medium container (250 g) costs £2.65.

A large container (350 g) costs £3.85.

Which of these options represent the best value?

Small
Medium
EDDIE SAYS
All of these weights can be changed easily to 50 g so that they can be compared. (Although you could easily change them all to 1 g if you prefer.) Small: 53 p per 50 g (159 ÷ 3) Medium: 53 p per 50 g (265 ÷ 5) Large: 55 p per 50 g (385 ÷ 7) So the best value is actually either the small or medium container, as they both cost exactly the same per 50 g. You can now find the costs of single units within larger packs, so that you can compare prices and decide which options represents the best value purchase - a great skill to have!
• Question 10

1 doughnut costs 40 p and a pack of 3 costs £1.23.

Which option represents the best value?

1 doughnut
EDDIE SAYS
Firstly, we need to find the cost of 1 doughnut in each scenario: 1 doughnut costs 40 p 3 doughnuts cost 123 p, so 1 doughnut costs 41 p (123 ÷ 3) Which option represents better value, 40 p or 41 p? The single doughnut represents the best value, as a single doughnut costs slightly less than it does in the 3-pack.
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