Changing the Subject in an Equation or Formula

In algebra we will learn how to find the value of the variables by changing the subject in an equation or formula using the balance method.

To find the value of the variable using change of subject of formula and method of substitution:

The process of finding the value of algebraic expression by replacing the variables by the given value is called the method of substitution.

In this,

  • Make the required variable as the subject.

  • Substitute the values of all the variables except the subject.

  • Now simplify and find the value of the subject.

Worked-Out Examples on Changing the Subject in an Equation or Formula

1. In the formula P = 2(l + b), find b when P = 36 cm and l = 10 m

Solution:

P = 2 (l + b)

P = 2l + 2b

P - 2l = 2b

(P - 2l)/2 = 2̶b/2̶

i.e., b = (P - 2l)/2

b = (36 - 2 × 10)/2

b = (36 - 20)/2

b = 1̶6̶/2̶

b = 8

2. Given A = P {1 + (r/100)}ⁿ make r as the subject.

Given A = 1102.50 P = 1000 n = 2, find r.

Solution:

A = P {1 + (r/100)}ⁿ

A/P = {1 + (r/100)}ⁿ

(A/P)^1/n = {1 + (r/100)}

(A/P)^1/n - 1 = r/100

100 {(A/P)^1/n - 1} = r

Therefore, 100 {(A/P)^1/n - 1}

Substituting the values of A, P and n we get;

r = 100 {(1102.50/1000)^1/2 - 1}

= 100 {(110250/1000)^1/2 - 1}

= 100 {(441/400)^1/2 - 1}

= 100 [{(21/20)²}^1/2 - 1]

= 100 {(21/20)^{2 × 1/2} - 1}

= 100 {21/20 - 1}

= 100 {(21 – 20)/20}

= 1̶0̶0̶ × 1/2̶0̶

= 5