Substituting into Formulae

Substituting into Formulae

Substitution is the replacement of variables (letters) in an expression with numbers. An expression of 4a means 4 x a: if a is known to have a value of 3, then replacing a gives 4 x 3 (=12).

Remember that there is a hidden times sign between the the number 4 and the letter a.

An expression may have more than one variable. For example, 3(a + 2b) has two variables: a and b. If a = 4 and b = 5, then substituting these values into the expression:

3(a + 2b)

= 3(4 + 2 x 5) (replacing a with 4 and b with 5)

= 3(4 + 10) (multiply 2 x 5 first: BIDMAS)

= 3 x 14 = 42.

Substitution is commonly used when evaluating formulae. The area of a rectangle is given by A = l x w, where A is the area, l is the length and w is the width. If the length of a rectangle is 6cm, and the width is 4cm, then the area is:

A = l x w

A = 6 x 4 (6 replaces l and 4 replaces w)

A = 24cm2

Example 1

The calculation of tax paid for income above £11,000 is given by the formula

T = (i - 11000) x 0.2

where T is the tax due and i is the income. What tax is due on an income of £23,400?

T = (i - 11000) x 0.2

T = (23400 - 11000) x 0.2

T = 12400 x 0.2 = 2480