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Algebraic formulae - EduqasCreating formula

Formulae are used in everyday life, from working out areas and volumes of shapes to converting units of measurement. Knowing how to use and rearrange formulae are very useful skills.

Part of MathsAlgebra

Creating formula

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 ÂŁ40, plus an hourly rate of ÂŁ18. 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 ÂŁ40 plus ÂŁ18 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 ÂŁ76.

Example 2

On a given day the plumber charges ÂŁ130. 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 ÂŁ130:

\(130 = 40 + 18h\)

Solve the equation:

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

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

The plumber worked for 5 hours to earn ÂŁ130.

Question

A worker's daily pay (\(P\)) depends on the amount of hours worked (\(h\)), the rate they are 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 ÂŁ9 per hour and who receives ÂŁ5 in bonuses will earn.

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Changing the subject of a formula
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Substitution

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