Creating formulae

Formulae are created for something that is calculated often.

For instance, plumbers often apply a call out charge plus an hourly rate to their customers. Writing a formula for the total cost of a job would be useful for a plumber so that they could quickly calculate costs for their customers more easily. Once a formula is written, the plumber would only need to input how long the job would take in hours, and come up with a total cost to quote very easily.

Example 1

A plumber has a call out fee of £40, plus an hourly rate of £18. Write a formula to calculate the cost of any job and calculate the cost of a job estimated to take 2 hours.

The total cost (\(T\)) would be equal to the call out charge of £40 plus £18 for every hour (\(h\)) worked.

This can be written as: \(T = 40 + 18h\)

Now, the total cost for customers can be worked out easily by substituting the number of hours the job will take.

A job estimated to take 2 hours can be calculated like this:

\(T = 40 + 18h\)

Substitute the number of hours as 2 hours:

\(T = 40 + 18 \times 2 = 40 + 36 = \pounds 76\)

Use BIDMAS to complete the multiplication before the addition.

A two hour job would cost £76.

Example 2

On a given day the plumber charges £130. How long did the plumber work for?

This time, it is not the total cost (\(T\)) that is to be calculated but the hours (\(h\)). In this instance the formula will need to be solved to find \(h\):

\(T = 40 + 18h\)

Substitute the total cost as £130:

\(130 = 40 + 18h\)

Solve the equation:

First, subtract 40 from both sides: \(90 = 18h\)

Next, divide both sides by 18: \(5 = h\)

The plumber worked for 5 hours to earn £130.

Question

A worker's daily pay (\(P\)) depends on the amount of hours worked (\(h\)), the rate he or she is paid per hour (\(r\)) and any bonus that is earned (\(b\)).

Write a formula for the pay of the worker, and calculate how much a person who works for 8 hours at a rate of £9 per hour and who receives £5 in bonuses will earn.

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Algebraic formulae - AQACreating formulae