# Ex.2.4 Q1 Linear Equations in One Variable Solution - NCERT Maths Class 8

## Question

Amina thinks of a number and subtracts \(\begin{align}\frac{5}{2}\end{align}\) from it. She multiplies the result by \(8\). The result now obtained is \(3\) times the same number she thought of. What is the number?

## Text Solution

**What is known?**

i) \(\begin{align}\frac{5}{2}\end{align}\) is subtracted from a number

ii) Then multiplied by \(8\)

iii) Result is \(3\) times the actual number

**What is unknown?**

Number thought of by Amina

**Reasoning:**

Assume the number to be a variable. Apply the conditions sequentially to form a linear equation.

**Steps:**

Let the number be \(x\).

According to the given question,

\[\begin{align}{8\left( {x - \frac{5}{2}} \right) = 3x} \\{\,\,\,\,8x - 20 = 3x}\end{align}\]

Transposing \(3x\) to LHS and \(−20\) to RHS, we obtain

\[\begin{align}{8x - 3x = {\text{ }}20} \\{\,\,\,\,\,\,\,\,\,\,\,5x = 20}\end{align}\]

Dividing both sides by \(5\), we obtain

\[x = 4\]

Hence, the number is \(4\).