How to solve linear equations .. some of them you'll solve without really thinking about!
Suppose you bought a CD for £8 and then two books at the same price. The total cost is £25 and, with a little bit of arithmetic, you might work out the price of each book is £8.50.
Mathematicians like to call these “linear equations” and they look something like:
2B + 8 = 25
(where ‘B' stands for ‘books')
Working with linear equations can get a little complex and there are a couple of rules:
- work down the page
- put the equals sign in the middle
- always remain in balance
- whatever you do to one side – you need to do to the other
Click here to try the quick test QT Linear Equations
Most of the exam questions for linear equations are based on
- mobile phone contracts
- temperature conversion
- travel money
They are all much the same and usually involve comparing two offers.
Here's some brief notes:
Always a favourite and goes something like
“A plan costs £30 per month plus 1p per message – write a linear equation”
The monthly cost would be: 0.01 x total messages + 30 or, tidying up and written as a linear equation:
£ = 0.01M + 30
(Note the conversion to the same units ie 1p per message = £0.01 per message)
Converting Fahrenheit into degrees Celsius is an example of a linear function. You need to subtract 32 from the Fahrenheit and the multiply the result by 5/9. There are a couple of different ways of writing this formula but it amounts to the same calculation.
Degrees C = (5/9) x (F – 32)
Degrees C = (F – 32) / 1.8
Something along the lines of
“You get paid £8 per hour and work for ‘x' hours per week. Tax is 8% of your pay. Write a linear equation to describe your pay.”
Total pay = 8'x' – 8%
or, tidying up:
Total Pay = 0.92 ( 8 ‘x' )
as it's neater to multiply by 0.92, which is the decimal equivalent of 100% – 8% … although the first equation is fine.
Fairly typically a currency conversion such as dollars $ to pounds £. As of beginning October 2012 there were $1.6074 to the £ so a linear equation would be:
£ = 1.6074 x $
or, tidying up:
£ = 1.6074$