# 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 ( ) would be equal to the call out charge of £40 plus £18 for every hour ( ) worked.

This can be written as:

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:

Substitute the number of hours as 2 hours:

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 ( ) that is to be calculated but the hours ( ). In this instance the formula will need to be solved to find :

Substitute the total cost as £130:

Solve the equation:

First, subtract 40 from both sides:

Next, divide both sides by 18:

The plumber worked for 5 hours to earn £130.

Question

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

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.

Multiply the amount of hours worked by the rate of pay and then add on the bonus.

This can be shown by writing a formula.

Using the letters given in the question gives:

The employee works 8 hours per day for an hourly rate of £9. The bonus they have earned is £5.

Substituting these values into the formula gives: