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y
( c) 1.8 = Think and Answer
.
36
1
3.6 × 1.8 = y (Transposing 36 to LHS) Kavya was solving a linear
.
36 18 648 equation 11x + 19 = 41, in steps
⇒ y = × = = 6.48 ⇒ y = 6.48
10 10 100 as shown below.
So, y = 6.48 is the required solution. 11x + 19 = 41

Verification: LHS = 1.8 Step 1: 11x = 41 – 19
Step 2:
11x = 22
y 648
.
RHS = = = 1.8 Step 3: 11x = 2
36 36 2
.
.
⇒ LHS = RHS, hence verified. Step 4: x = 11
( d) 16 + 4p = 24 What should Kavya do to correct
⇒ 4 p = 24 – 16 (Transposing 16 to RHS) her mistake?
8
⇒ 4 p = 8 ⇒ p = (Transposing 4 to RHS)
4
⇒ p = 2
So, p = 2 is the required solution.
Verification: LHS = 16 + 4p = 16 + 4 × 2 = 16 + 8 = 24
RHS = 24 ⇒ LHS = RHS, hence verified.

Applications of Linear Equations in Real Life

By applying the concept of linear equations, various real-life problems can be solved. To solve a
problem, we convert it into a linear equation and then solve the equation.
Consider the following word problem:
Sita and Gita are friends. Both have some marbles. The number of marbles having Sita is 3 more
than twice the number of marbles having Gita. If both have 27 marbles altogether, find the number
of marbles both have.

This problem can be solved by expressing number of marbles having Sita in terms of number of
marbles having Gita.

Let the number of marbles with Gita be x. Let us now find out number of marbles with Sita in
term of x.

As the number of marbles with Sita is three more than the twice the number of marbles with Gita.
So, the number of marbles with Sita is (2x + 3).
Now, it is given that the sum of the number of marbles with Sita and Gita = 27
So, x + (2x + 3) = 27 ⇒ 3x + 3 = 27
We have converted the given problem into a linear equation in one variable.

Now, if we solve it, we can find out the number of marbles with Sita and Gita
3 x = 27 – 3 (Transposing 3 to RHS)
⇒ 3 x = 24 ⇒ x = 8 (Dividing both sides by 3)

So, the number of marbles with Gita is 8.
And, the number of marbles with Sita = 2x + 3 = 2 × 8 + 3 = 16 + 3 = 19
Thus, the number of marbles with Gita is 8 and the number of marbles with Sita is 19. You can
easily see that the sum of marbles is 8 + 19 = 27.

39 Linear Equations in One Variable