Percentages | 7 Amazing Solutions
Percentages – Introduction
In this article we are going to look at percentages. For the purposes of this article it is going to be assumed that you know what is meant by percentages and how to perform the necessary calculation.
What is going to be looked at is more worded problems that have been taken from a foundation paper. The questions that are going to be looked at are of grade 3 equivalent. So if you are doing the foundation paper and are looking to secure a minimum of a grade 4 then it is important that you are able to confidently answer questions that cover the topic of percentages.
This article is going to cover 7 questions of varying difficulty but it needs to be remembered that they are all graded at a 3. Some are short in terms of the amount of text within the question and there are other questions where there is a little more to read.
It is important not to be put off by these more worded questions but to deal with each sentence at a time and to perform the required calculations.
Percentages - Questions 1 - 3
Let us start with a free warm up questions:
Q1
With this question you must show all your working to obtain full marks. You cannot just pick one and hope it is correct. Even if you did pick the correct one without showing any of your work, you would obtain no marks.
Here you simply need to calculate the percentage amounts of each and to then make a comparison as shown here:
25 \% \text { of } 90\begin{aligned} & 10 \% \text { of } 90=9 \\ & 20 \% \text { of } 90=18 \\ & 5 \% \text { of } 90=4.5 \end{aligned}
\therefore 25 \% \text { of } 90=18+4 \cdot 5=22 \cdot 5
28 \% \text { of } 82
10 \% \text { of } 82=8 \cdot 2
20 \% \text { of } 82=16.4
1 \% \text { of } 82=0.82
8 \% \text { of } 82=6.56
\therefore 28 \% \text { of } 82=16 \cdot 4+6.56=22.96
This means 28 \% \text { of } 82 is greater.
What is important as well for a question like this is that once you have done all the necessary work, actually then give a suitable conclusion as to which is the larger value.
Q2.
Here you need to find 30% of £130 and compare this to £40 as shown here:
The difference = £40 – £39 = £1
Notice that the question is asking for a “difference” in the bonus amounts.
Q3.
If 25% of the people at the cinema are children then this means that the number of adults at the cinema must be the other 75%. Knowing this you can then determine what 100% is , which is the total number of people at the cinema.
\begin{aligned} & 75 \%=48 \\ & 25 \%=16 \\ & 100 \%=64 \end{aligned}Percentages - Questions 4 - 5
Q4.
Here you need to determine what 3% is of £34,000 and to then add this amount back.
This is shown here:
\begin{aligned} 10 \% \text { of } 34000 & =3400 \\ 1 \% \text { of } 34000 & =340 \\ 3 \% \text { of } 34000 & =340 \times 3=1020 \end{aligned}New Pay = 34000+1020=35,020
Q5.
Questions like this are quite common. First you need to determine what 15% actually is. This amount is the deposit that has been paid. Because this amount has been paid already, it needs to be subtracted from the total. You will then have an amount outstanding and to determine the number of months that it will take to make the repayment can be done by division as shown here:
\begin{aligned} 10 \% \text { of } £ 540 & =£ 54 \\ 5 \% \text { of } £ 540 & =£ 27 \end{aligned}15% of £540 = £54 + £27 = £81
Balance = £540 – £81 = £459
Number of months = £459/£17 = 27
This question has required the need to perform percentage calculations, subtraction and also division. And it is these steps that you need to recognise are required.
Percentages – Questions 6 – 7
Q6.
Here you need to find what 35% of 420 is and then you can add this number to the 120. You can then determine the number of lemon cakes as shown here:
\begin{aligned} 10 \% \text { of } 420 & =42 \\ 30 \% \text { of } 420 & =42 \times 3=126 \\ 5 \% & \text { of } 420=21 \\ \therefore 35 \% \text { of } 420 & =126+21=147 \end{aligned}The number of lemon cakes = 420-120-147=153
Q7.
To answer this type of question you need to work out the cost from each shop and to then make a suitable comparison and conclusion. Note the question has stated “you must show how you get your answer”. Not doing this means that without any working you get zero marks.
Shop B calculations are shown here:
Buy 4 Get 2 Free
4 \times 65=260=£ 2.60Shop A calculations are shown here:
\begin{aligned} & 6 \times 48=288 \\ & 10 \% \text { of } 288=28.8 \text { pence } \\ & 5 \% \text { of } 288=14.4 \text { pence } \\ & 288-14.4=273.6 \text { pence }=274 \text { pence }=£ 2.74 \end{aligned}This is the type of work that you should be showing and you always need to keep your work neat and logical. Always be on the side of the examiner so they can mark your work accurately in order to help yourself get the best possible grade.
Keep practising these questions and try them again without looking at the answers. We will be posting more similar articles in the near future to help you succeed with your GCSE Maths.