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4.10 G) Unit Pricing – Part 2
4.10 G) Unit Pricing – Part 2
The content in this section builds on the content that was discussed in the previous section. Make sure that you have covered the content in the previous section before working through the content in this section (click here to be taken through to the previous section).
Unit Pricing for Grams or ml
For the first example, it was quite easy to work out which option was the best value for money. This was because the options were all whole numbers and we could easily work out what the cost was for one (in the example in the previous section, we worked out what the cost was for one can).
However, you can be asked questions involving unit pricing when the units that you are finding the cost for are less clear. This usually happens when you are finding the unit prices for quantities that are in grams or ml. For quantities involving grams, you could find the cost per gram, per 100 grams, or per kilogram. For quantities involving millilitres, you could find the cost per millilitre, per 100 millilitre or per litre.
An example of this is purchasing chicken off an online supermarket. There are a variety of different sized packs that you can purchase chicken in. Two of these options are shown below:
For the first example, it was quite easy to work out which option was the best value for money. This was because the options were all whole numbers and we could easily work out what the cost was for one (in the example in the previous section, we worked out what the cost was for one can).
However, you can be asked questions involving unit pricing when the units that you are finding the cost for are less clear. This usually happens when you are finding the unit prices for quantities that are in grams or ml. For quantities involving grams, you could find the cost per gram, per 100 grams, or per kilogram. For quantities involving millilitres, you could find the cost per millilitre, per 100 millilitre or per litre.
An example of this is purchasing chicken off an online supermarket. There are a variety of different sized packs that you can purchase chicken in. Two of these options are shown below:
The option on the left is 640 g and it costs £4.20. The option on the right is 1 kg and it costs £6. You can see the unit cost next to the prices. The unit cost is the cost per kilogram. The option on the left is £6.56 per kg, and the option on the right is £6 per kg. £6 is cheaper than £6.56, which tells us that the option on the right is the better value for money.
It does not matter what unit pricing you use when you are carrying out your calculations. You just need to make sure that the unit pricing is the same for all of the options. For example, all of the unit pricing could be in per kg. You should never have one of the options in per kg and the other option in per 100g. This is because different unit pricing will mean that you cannot compare the costs, and therefore, cannot determine which option is the better value for money.
It does not matter what unit pricing you use when you are carrying out your calculations. You just need to make sure that the unit pricing is the same for all of the options. For example, all of the unit pricing could be in per kg. You should never have one of the options in per kg and the other option in per 100g. This is because different unit pricing will mean that you cannot compare the costs, and therefore, cannot determine which option is the better value for money.
Example 1
There are two packs of flour. A 200g bag that costs 90 pence and a 500g bag that cost £2.50. Which one is better value for money?
The question does not ask us the find a specific unit price. This means that we can choose the unit that we want to work out the price for; we could work out the price per gram, per 100 grams or per kilogram etc. It does not matter which unit we choose, and this is because the option that is better value for money will always be cheaper irrespective of the specific unit that you choose. I am going to work through 3 different units; price per 1 g, price per 100 g and price per 1 kg.
There are two packs of flour. A 200g bag that costs 90 pence and a 500g bag that cost £2.50. Which one is better value for money?
The question does not ask us the find a specific unit price. This means that we can choose the unit that we want to work out the price for; we could work out the price per gram, per 100 grams or per kilogram etc. It does not matter which unit we choose, and this is because the option that is better value for money will always be cheaper irrespective of the specific unit that you choose. I am going to work through 3 different units; price per 1 g, price per 100 g and price per 1 kg.
Price per gram
The first specific unit that I am going to look is the price per gram. In order to find out the price per gram, we divide the price of the flour by the number of grams.
The first specific unit that I am going to look is the price per gram. In order to find out the price per gram, we divide the price of the flour by the number of grams.
The 200g bag cost 90p, which means that the price per bag in pence is:
For the first option, the price per gram is 0.45p.
Let’s do the same for the 500g bag of flour. The 500g bag cost £2.50. I have chosen my unit price to be in price per gram in pence and this means that we need to convert the £2.50 into pence. There are 100 pence in a pound. Therefore, we find the number of pence in £2.50 by multiplying by 100, which gives 250 pence. We can now sub in 250 pence and 500g into the formula.
Let’s do the same for the 500g bag of flour. The 500g bag cost £2.50. I have chosen my unit price to be in price per gram in pence and this means that we need to convert the £2.50 into pence. There are 100 pence in a pound. Therefore, we find the number of pence in £2.50 by multiplying by 100, which gives 250 pence. We can now sub in 250 pence and 500g into the formula.
For the second option, the price per gram is 0.5p.
The 200g bag of flour is 0.45 pence per gram and the 500g bag of flour is 0.5 pence per gram. 0.45 is less than 0.5, which means that the 200 g bag is better value for money.
Working out the price per gram is fairly straightforward when we have a calculator, but it could become quite tricky if we did not have one.
The 200g bag of flour is 0.45 pence per gram and the 500g bag of flour is 0.5 pence per gram. 0.45 is less than 0.5, which means that the 200 g bag is better value for money.
Working out the price per gram is fairly straightforward when we have a calculator, but it could become quite tricky if we did not have one.
Price per 100g
We can also work out the cost per 100g. We do this by dividing the cost by the number of 100 grams in the bag.
We can also work out the cost per 100g. We do this by dividing the cost by the number of 100 grams in the bag.
The first option was a 200g bag that costs 90p. There are 2 one hundreds in 200g. Therefore, we can work out the cost per 100g by dividing 90p by 2.
For the first option, the cost per 100g is 45p.
We do the same for the second option. The second option is 500g, which is 5 lots of 100g. We want to answer to be in terms of pence, so we divide 250p by 5.
We do the same for the second option. The second option is 500g, which is 5 lots of 100g. We want to answer to be in terms of pence, so we divide 250p by 5.
The second option is 50p per 100g.
The first option is better value because 45p is less than 50p.
The first option is better value because 45p is less than 50p.
Price per kg
If you were not a fan of the previous two methods, you can find out which bag is cheaper by purchasing the same quantity from each of the different sized bags and then comparing how much it would cost you. When you are choosing the quantity, you choose the lowest common multiple between the two quantities that you are given; the lowest common multiple is the first number that two or more numbers go into. The two quantities that we are given in the question are 200g and 500g. The lowest number that goes into both 200 and 500 is 1,000. Therefore, I am going to work out the cost of purchasing 1,000g from both of the options; this can also be viewed as the cost per kilogram.
Let’s do this for the first option. The first option was a 200g bag that cost 90p. We will need to buy 5 packs of flour in order to purchase 1,000g of flour. We work out the cost of buying 1,000g of flour from the first option by multiplying £0.90 (90p) by 5.
If you were not a fan of the previous two methods, you can find out which bag is cheaper by purchasing the same quantity from each of the different sized bags and then comparing how much it would cost you. When you are choosing the quantity, you choose the lowest common multiple between the two quantities that you are given; the lowest common multiple is the first number that two or more numbers go into. The two quantities that we are given in the question are 200g and 500g. The lowest number that goes into both 200 and 500 is 1,000. Therefore, I am going to work out the cost of purchasing 1,000g from both of the options; this can also be viewed as the cost per kilogram.
Let’s do this for the first option. The first option was a 200g bag that cost 90p. We will need to buy 5 packs of flour in order to purchase 1,000g of flour. We work out the cost of buying 1,000g of flour from the first option by multiplying £0.90 (90p) by 5.
The cost per 1,000g (or per 1 kg) for the first option is £4.50.
We now do the same for the second option, which was 500g of flour for £2.50. In order to have 1,000g of flour, we would need 2 bags. Therefore, we find the cost of 1000g by multiplying the cost of one bag (£2.50) by 2.
We now do the same for the second option, which was 500g of flour for £2.50. In order to have 1,000g of flour, we would need 2 bags. Therefore, we find the cost of 1000g by multiplying the cost of one bag (£2.50) by 2.
The cost per 1,000g (or 1 kg) is £5.
We now compare the costs for the different options. The cost per 1,000g for the 200g bag was £4.50 and the cost per 1000g for the 500g bag was £5. £4.50 is less than £5. Therefore, the first option is better value for money.
We now compare the costs for the different options. The cost per 1,000g for the 200g bag was £4.50 and the cost per 1000g for the 500g bag was £5. £4.50 is less than £5. Therefore, the first option is better value for money.
Final Note
There is no set way to compare the cost for quantities like grams and ml. Sometimes it will be easier to find the price per g or per ml; this is especially the case if you have a calculator. And, sometimes it will be easier to find the cost for a higher quantity, such as 1,000g or 1,000 ml; this is usually the case if you do not have access to a calculator.
There is no set way to compare the cost for quantities like grams and ml. Sometimes it will be easier to find the price per g or per ml; this is especially the case if you have a calculator. And, sometimes it will be easier to find the cost for a higher quantity, such as 1,000g or 1,000 ml; this is usually the case if you do not have access to a calculator.