GCSE Maths Utility Bills - How To Solve Them
Introduction
GCSE Maths Utility bills refer to the amount of money that is paid for water, gas and electricity. These utilities are provided by a range of companies and there are usually news stories relating to various providers especially when it comes to increasing prices.
The actual calculation needed is not difficult but the process is often misunderstood.
GCSE Maths Utility Bills - An Example
Take a look at the following GCSE Maths Utility Bills question:
In answering questions like this there are always two things that you need to look at.
- The meter reading at the beginning
- The meter reading at the end
From this question, the meter reading at the start is 8569 and at the end it is 9872.
The question wants the cost of gas used. And it is this wording of the question that should help you determine the calculation that is needed.
Here you need to perform a subtraction in order to find the number of units that have been used. In this case it is 9872 -8569 = 1303 units.
You know the number of units used. Next you need to find the cost. The cost per unit is 44p so the total cost is 1303 x 44p = 57,332.
It is at this stage that you need to be very careful and to insert the correct units. Sometimes the question paper will have a £ symbol where it wants you to insert the answer, sometimes there will be nothing. But it is important to note that the number of units has been multiplied by 44 pence so 57,332 is an amount in pence.
Always be checking your answer to see if it appears to be sensible. For this particular case the cost in pounds would be £573.32.
Example
Consider the following GCSE Maths Utility Bills question:
Here there is no meter reading simply the units used.
First determine the cost of the units used as follows (remembering to take care of the units): 367 x 5.84p = 2,143.28p = £21.43
The question also states that there is a fixed month charge, and this is payable whether or not any electricity is used or not.
The total for the month is £21.43 + 6.14 = £27.57
Question Practice
Try the following question on your own before looking at the solution.
Question Practice Solution
So how did you get on? Hopefully you found the answer to be £67.34.
In this question a meter reading is provided so you should start by actually finding the number of units used and this is done by subtraction; units used = 80305 – 79721 = 584 units.
How this question differs is the information that is given with regards to how payment is made.
The first 70 units cost 21.3p which is a total of 70 x 21.3 = 1,491p = £14.91
Because 70 units have been accounted this then leaves 584 – 70 = 514 units and this are charged at 10.2p for each unit to give a total cost of 514 x 10.2 = 5242.8p = £52.43
The total bill is therefore £52.43 + £14.91 = £67.34
When it comes to bills the main thing to do first is to determine the units used. Go look at an actual bill and you will see a current reading, a previous reading as well as information on the units used for that particular source of energy.
GCSE Maths Utility Bills is a practical and real application of how maths is used in the real world. The next time a bill arrives at your home and take a look at the structure and layout and how the total cost is then calculated.
This is a fairly straightforward topic and this can appear on both the foundation and higher paper. It is an area where it is possible to achieve full marks but you need to make sure that you are displaying all your work.