TRABAJANDO CON FÓRMULAS

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We often use formulas without even noticing. For example, we might convert miles to km by multiplying by 1.6, or find the circumference of a circle by multiplying pi by the diameter.

km = 1.6 x miles is an example of a formula.

Using formulas

We have already seen that km = 1.6 x miles and C = × d are examples of formulas. There are many others that we use regularly in other subjects. Sometimes we have to construct our own formula:

Example

A taxi firm charges 50p per mile plus a fixed charge of £2.00. Write down a formula for the cost (C) of hiring this taxi to travel ‘n’ miles.

Solution

• Travelling 1 mile would cost £2 + 50p.
• Travelling 2 miles would cost £2 + 2 x 50p.
• Travelling 3 miles would cost £2 + 3 x 50p.

So travelling for 'n' miles will cost £2 + n x 50p.

The formula is C = £2 + (n x 50p)

Question

A rectangle has a width of x and a length of 2x.

Write down a formula for the perimeter (P) in terms of x.

Substitution

To recap, the cost (C) of hiring this taxi to travel ‘n’ miles, when a taxi firm charges 50p per mile plus a fixed charge of £2.00 is:-

C = £2 + (n x 50p)

To find the cost of the taxi for a journey of 20 miles, replace 'n' with 20.

C = £2 + (20 x 50p)

C = £2 + £10

C = £12

Question

What is the cost of hiring this taxi for 16 miles?

Changing the subject of a formula

The formula for finding the circumference of a circle is C = 2r. So it is easy to find the circumference if we know the radius.

What happens, though, if we know the circumference but want to know the radius?

In this case we can rearrange to make r the subject of the formula.

C = 2r, so we divide both sides by 2

or

Question

The equation of a straight line is y = mx + c

Rearrange the formula to make 'c' the subject.

Answer

y - mx = c

or

c = y - mx

[To work this out: y = mx + c, so subtract mx from both sides.]