ALGEBRA-FORMULAS AND EQUATIONS

USING FORMULAE 

We often use formulae 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 formulae

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

Example

SolutionA taxi firm charges £0.50 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.

• It costs £2 + £0.50 to travel 1 mile.
• It costs £2 + 2 x £0.50 to travel 2 miles.
• It costs £2 + 3 x £0.50 to travel 3 miles.

So travelling for 'n' miles will cost £2 + n x £0.50.

The formula is C = £2 + (n x £0.50).

Note: £0.50 = 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.

Answer

P = 2x + x + 2x + x

Did you remember to include all 4 sides?

So P= 6x

Substitution

To recap, the cost (C) of hiring this taxi to travel 'n' miles, when a taxi firm charges £0.50 per mile plus a fixed charge of £2.00 is:-

C = £2 + (n x £0.50)

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

C = £2 + (20 x £0.50)

C = £2 + £10

C = £12

Question

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

Answer

£10

Remember that C = £2 + (16 x £0.50)

= £2 + £8

= £10

Changing the subject of a formula

The formula for finding the circumference of a circle is C = 2πr. 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 = 2πr, so we divide both sides by 2π

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.]

Question

The formula connecting °C and °F is:

Rearrange the formula to make 'F' the subject.

Answer

[Multiply by 9] 9C = 5(F − 32)

[Divide by 5]   = F − 32

[Add 32]  + 32 = F

So F =  + 32

Note:  is also correct.

CHANGING SUBJECT OF FORMULA-HIGHER

Sometimes we will…