Question

Anu thinks of a rational number and subtract 2/5 from it she multiply its results by 6 and obtain a number that is 3 more than 5 times the original number find the number that she thought of

Answer 1

Let the rational number thought by Anu, be:

$\dfrac{p}{q}$

As per question statement:

1. Subtract $\frac{2}{5}$ from the number i.e.

$\dfrac{p}{q} - \dfrac{2}{5}$

2. Multiply the results by 6:

$(\dfrac{p}{q} - \dfrac{2}{5}) \times 6 ...... (1)$

3. Result obtained is 3 more than 5 times the original number:

$3 + 5 \times \dfrac{p}{q} ...... (2)$

Equating (1) and (2):

$(\dfrac{p}{q} - \dfrac{2}{5}) \times 6 = 3 + 5 \times \dfrac{p}{q} \\\Rightarrow 6\times \dfrac{p}{q} - \dfrac{12}{5} = 5 \times \dfrac{p}{q} + 3\\\Rightarrow 6\times \dfrac{p}{q} - 5 \times \dfrac{p}{q} = \dfrac{12}{5} + 3\\\Rightarrow \dfrac{p}{q} = \dfrac{12+15}{5}\\\Rightarrow \dfrac{p}{q} = \dfrac{27}{5}$

So, the fraction that Anu thought of is:

$\dfrac{p}{q} = \dfrac{27}{5}$

Answer 2

The original rational number is $\frac{27}{5}$ .

Step-by-step explanation:

We are given that Anu thinks of a rational number and subtract 2/5 from it. Then she multiply its results by 6 and obtains a number that is 3 more than 5 times the original number.

Let the original rational number be $\frac{x}{y}$ .

Now according to the question, first condition states that Anu thinks of a rational number and subtract 2/5 from it, that means;

                       $\frac{x}{y} -\frac{2}{5} = \frac{5x-2y}{5y}$

Then, she multiply its results by 6, that means;

                      $\frac{5x-2y}{5y} \times 6 = \frac{30x-12y}{5y}$

Now, she obtains a number that is 3 more than 5 times the original number, that means;

                      $\frac{30x-12y}{5y} = 3 + (5 \times \frac{x}{y} )$

                       $\frac{30x-12y}{5y} = \frac{3y +5x}{y}$

                       $\frac{30x-12y}{5} = {3y +5x}$

                       $30x-12y} = {15y +25x}$

                       $30x - 25x = 15 y+12 y$

                           $5x = 27 y$

                            $\frac{x}{y} =\frac{27}{5}$

Hence, the original rational number was $\frac{x}{y} =\frac{27}{5}$ .