## What you need to know

### Best Buys

Go to any supermarket and you’ll see all kinds of different brands selling the same product – and they often have various offers on as well. In those scenarios, it isn’t always obvious which product gives the best value for money. This essentially boils down to asking the question:

“If I buy the same amount of each product, which one will cost me less?”

Answering this question is what ‘best buy’ questions are all about.

### Example 1: Best Buys

Three different brands of washing powder are on sale. Their prices are shown below. Work out which brand provides the best value for money.

In order to compare the prices of each of these brands, we will work out how much it costs to buy 100g of each brand. Then, the smallest value will tell us what the best value for money.

Brand A: The price shown is for 400g, so if we divide the value by 4, we get

\text{Brand A cost of 100g }=2.56\div 4=\pounds 0.64Brand B: The price shown is for 750g, so this time we want to divide the value by 7.5. If you’re not sure how we get the value 7.5, it’s the number of hundreds that go into 750:

750 \div 100=7.5So, we get

\text{Brand B cost of 100g }=5.10\div 7.5=\pounds 0.68Brand C: The price shown is for 1.2kg, so let’s first convert that into grams:

1.2\times 1,000=1,200\text{ g}So, the price shown is for 1,200, which is equal to 12 \times 100. Therefore, we get

\text{Brand C cost of 100g }=7.38\div 12=\pounds 0.615Comparing the 3 values, we can see that the cheapest price of 100g is brand C. Therefore, brand C offers the best value for money.

**Note:**whilst you can’t actually have £0.615 (because that would involve having half a penny), it’s okay to use that value to compare prices in a best buy questions.

### Example 2: Best Buys

Two different sized cans of coconut milk are on sale in a shop.

The smaller can currently has an offer that reads

“Buy ONE get the second HALF PRICE!”

Considering this offer, work out which size can of coconut milk currently gives the best value for money.

In this situation, we need to make sure to apply any offers that are shown before we can have any values to compare. Again, we’re going to look at the cost per 100g.

Smaller can: We can get one 300g can for £1.20, and a second 300g can for half price:

1.20\div 2=\pounds 0.60Therefore, in total, we can get two cans, which amounts to 600g, for

1.20+0.60=\pounds 1.80This means that

\text{smaller can: cost per 100g }=1.80\div 6=\pounds 0.30Bigger can: We can get one 500g can for £1.40. Therefore, we get that

\text{bigger can: cost per 100g }=1.40\div 5 =\pounds 0.28Comparing the two values of the “cost per 100g” we can clearly see that even when we consider the offer on the smaller can, the bigger can is better value for money.

### Example Questions

1) A supermarket sells two different brands of tomato purée. Work out which brand offers better value for money.

In this case, we can see that brand 2 contains 3 times as much as brand 1 (200\text{ ml} \times 3 = 600\text{ ml}), so if we calculate the cost of buying 3 containers of brand 1, that will be the same amount of tomato purée as one container of brand 2.

\text{600 ml of brand 1 costs }=\pounds0.80\times 3 = \pounds 2.40

This is more than £2.20, so we can see that brand 2 is better value for money.

2) Two different brands sell boxes of pencils.

Brand 1 releases a new offer:

“Get 30% more pencils for the SAME PRICE!”

Considering this offer, work out which brand offers better value for money.

The first thing we need to calculate in this question is how many pencils you can buy from brand 1 given that their offer states you get 30% more pencils for free.

30\%\text{ of }120 = 0.3\times 120=36\text{ extra pencils}

This means that for £4.20 you receive 120+36=156 pencils instead of 120.

The next step is to calculate how much each pencil costs for each brand.

If brand 1 sells 156 pencils for £4.20, then the price per pencil would be as follows:

\pounds4.20 \div 156 = \pounds0.0269……

If brand 2 sells 200 pencils for £6.00, then the price per pencil would be as follows:

\pounds6.00 \div 200 = \pounds0.03

As a result, when we compare the two offers, brand 1 is better value for money since the price per pencil is less.

3) Richard wants to compare the cost of strawberries in different supermarkets. He records the cost and size of a punnet of strawberries in 3 different supermarkets in the table below.

Work out which supermarket offers the best value for money on strawberries.

As all of these numbers are quite awkward, so it isn’t obvious how we could calculate a “cost per 100g” value for each supermarket. Instead, in this case, we’ll just find a cost per gram. The answers will be small and a bit more fiddly, but we can still look at them and see which is smallest.

Supermarket A:

2.40\div 215=\pounds 0.0111...\text{ per gram}

Supermarket B:

4.10\div 403=\pounds 0.0101...\text{ per gram}

Supermarket C:

\text3.40\div 297=\pounds 0.0114...\text{ per gram}

The price per gram for the three supermarkets is similar but, looking closely, we can see that supermarket B offers the best value for money.

4) Mr Smith pays £4.48 for 400g of Edam cheese and buys 250g of Gorgonzola. Gorgonzola costs £11.60 per kilogram.

a) how much does Mr Smith pay for the Gorgonzola?

b) which type of cheese is better value and by how much per gram?

a) If Mr Smith is buying 250g of Gorgonzola, then this is one quarter of a kilogram (1000\text{ grams} \div 250\text{ grams} = 4).

If Gorgonzola costs £11.60 per kilogram, then the cost of 250g can be calculated as follows:

\pounds11.60 \div 4 = \pounds2.09

b) In order to compare the prices of both cheeses, we need to work out how much each cheese costs per gram.

The price of Edam can be calculated as follows:

\pounds4.48 \div 400 = \pounds0.0112 \text{ per gram}

The price of Gorgonzola can be calculated as follows:

\pounds11.60 \div1000= \pounds0.0116\text{ per gram}

As a result, we can see that the Edam cheese is better value as it costs less.

To work out the difference per gram, it might be easier to change the prices in pounds per gram to prices in pence per gram.

\text{ Edam:}\pounds0.0112 \times 100 = 1.12\text{ pence per gram}

\text{ Gorgonzola:}\pounds0.0116 \times 100 = 1.16\text{ pence per gram}

The difference between one gram of Edam and one gram of Gorgonzola can be calculated as follows:

1.16 - 1.12 = 0.04 \text{ pence per gram}

5) Gary is looking for the most cost-effective taxi service in Leeds, and is trying to decide between the following 3 taxi firms:

AARDVARK TAXIS

Initial charge: £3.00

First mile: £3.80

Every additional mile: £1.60

A1 CABS

Initial charge: £3.80

Cost per mile: £1.80

ABC CABS

Cost per mile: £2.10

Order the 3 firms from best value to least value for an 11 mile journey.

An 11 mile journey with Aardvark Taxis is the trickiest of the three firms to calculate since the first mile is more expensive. Therefore, the first mile is £3.80 and the remaining 10 miles are charged at £1.60. The total cost of the journey can be calculated as follows:

\pounds3.00 + \pounds 3.80 + (\pounds1.60 \times 10) = \pounds22.80

An 11 mile journey with A1 Cabs can be calculated as follows:

\pounds3.60 + (11 \times \pounds1.80) = \pounds23.60

An 11 mile with journey with ABC Cabs can be calculated as follows:

11 \times \pounds2.10 = \pounds23.10

The best value company is Aardvark Taxis, the next best value is ABC Cabs, and the worst value is A1 Cabs.

### Worksheets and Exam Questions

#### (NEW) Best Buys Exam Style Questions - MME

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