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When am I Ever Going to Use Linear Equations!?

Often as a Maths teacher and tutor I get asked by my students “when will I ever use this, no one ever uses this in real life, do they?” The answer to this question is always yes, no matter the topic. Everything in GCSE or iGCSE Maths has real world applications often interesting and always important to the functioning of our modern economy.

Take linear equations, for instance, you will probably know them as either y=mx+c; those really boring questions in which you are given a table of co-ordinates that you have to plot on a graph; or the questions in which you are asked to find something like the gradient; or, the y-intercept of a line whose equation looks something like 2y-4x=8. What is the point of drawing a boring line graph or finding the gradient of an equation?

Well, one application which you may have already come across in the sciences are distance-time graphs. Formula 1 teams, for example, can discover the speed of their opponents by calculating the gradient of a distance-time graph. Similarly, Formula 1 teams can use simultaneous linear equations to predict the exact place and time that their driver will overtake an opposing team. Although even using linear equations, they would most likely still not be able to catch Lewis Hamilton!

Many businesses use systems of linear equations to model their operations. For instance, if McDonald’s were only to sell Cheeseburgers and Fries at 99p and 89p respectively, you could model the amount the amount of revenue that McDonald’s will make using a linear equation R=99x+89y, where x and y are the number of sales of Cheeseburgers and Fries respectively.

Modelling revenue in this way allows businesses to optimise the amount they produce according to restraints which can also be modelled with linear equations. For example, two linear inequalities could specify the supply and the demand for Cheeseburgers and Fries. One such restraint on supply could be that it costs McDonald’s 60p to make Cheeseburgers and 50p to make Fries, but the amount that McDonald’s spends to make Cheeseburgers and Fries has to be below £100, or 10000p, this could be modelled with the linear inequality 60x+50y < 10000. McDonald’s could then use graphical inequalities to determine the optimal number of Cheeseburgers and Fries to produce.

Thankfully for me, McDonald’s also makes Salad as well as Cheeseburgers and Fries. I hope I have demonstrated to you some of the interesting uses of linear equations, because these equations have many more applications and are integral to the fields of Business, Economics and Physics! And, who knows, maybe with enough of these McDonald’s salads I will be able to catch up to Lewis Hamilton…


5 Exciting Careers that Maths & Sciences can Lead to

Food Scientist

Walkers Crisps, Ben and Jerry’s Ice Cream and Mars Chocolates are all companies that hire Food Scientists to help them develop their new delicious sweets and treats.

Food Scientists are an important part in the research and development of new food products and many are hired as graduates who have just completed degrees in Chemistry or Biology. Understanding the structure of the various chemicals in your food is necessary to develop the best tasting foods for your enjoyment. A career as a Food Scientist would give you the opportunity to play a part in the production of your next favourite sweet or snack.

Software Developer

Software developers build apps and computer programs which are becoming more and more integral in our world. Software Developers are using their skills to bring about new ideas that are revolutionising the way we live our lives. Apps like Snapchat allow people to communicate in new ways and were envisaged and developed by young software developers like Bobby Murphy. Modern computers have made it so that anyone with an idea and programming skills can easily implement their ideas. Many Science and Maths degrees provide the opportunity to learn programming, but even at a younger age concepts such as Sets in GCSE Maths are integral to good programming.

Video Game Developer

Along with the programming skills that are necessary in video game development.

Many video games need to simulate physical environments and for this a good understanding of physical processes and mathematical modelling techniques are necessary. Games like Mario Kart on your Nintendo console, Gran Turismo for PlayStation and Forza on Xbox use GCSE Maths concepts like vectors to model the driving forces and velocities of their cars.

Data Scientist

Another new career which has really taken off in the new digital economy is the role of the Data Scientist. Many applications collect data on their users and the power of modern computers allows us to quickly process this data to generate insights into how people think and behave. For instance, a study of twitter data found that there are relationships between the words people use on twitter and their personality types. Data Science, is also becoming more and more important in Finance to predict the prices of stocks and shares. Of course, it goes without saying that a good Data Scientist needs a good grasp of statistics.

Forensic Scientist

Many criminal investigations would be insolvable without the assistance of Forensic Scientists. If you’re a fan of detective dramas or novels this may be the career path for you. Forensic Scientists use their scientific knowledge and skills to help law enforcement investigate crimes. Using their knowledge of biology mainly, they can analyse fingerprints and traces of DNA to generate clues about who may have been involved in a crime and how it happened.

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