How to solve linear equations – including word problems

Simon

12 years ago

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
salaries
travel money

They are all much the same and usually involve comparing two offers.

Here’s some brief notes:

Mobile phones

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)

Temperature conversion

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

Salaries

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.”

Which means

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.

Money

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$