**Best Buys** *Questions, Worksheets and Revision*

## What you need to know

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’ problems are all about.

Best Buy Questions

Example: 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 question.

Example: 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=180\text{g}This 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.

## Best Buys Questions

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

In this case, we can see that brand 2 contains 3 times as much as brand 1, so if we find the cost of buying 3 containers of brand 1, that will be the same amount as one container of brand 2.

\text{600 ml of brand 1, cost }=0.80\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 the best value for money.

Firstly, we need to work out how many pencils would be in brand 1’s box if there are 30% extra.

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

\text{new number of pencils in brand 1’s box }=120+36=156

Now we’re going to calculate the cost per pencil for each brand.

Brand 1:

\text{cost of 1 pencil }=4.20 \div 156=\pounds 0.0269...

Brand 2:

\text{cost of 1 pencil }=6.20\div 200=\pounds 0.031

Looking at the values, we can see that, when considering the offer as the question asks, brand 1 offers better value for money.

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, it isn’t obvious how we could get a “cost per 100g” value for each one. 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:

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

Supermarket B:

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

Supermarket C:

\text{cost per gram }=3.40\div 297=\pounds 0.0114...

So, the numbers are all pretty small and quite close to each other, but looking 3 significant figures into each we can see that supermarket B offers the best value for money.