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 $$4$$.

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