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

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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?

 Video Solution
Linear Equations
Ex 2.4 | Question 1

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 \(4\).