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A rational number is such that when you multiply it by 1/4 and add 2/5 to the product, you get 27/5. What is the number❓

Question

A rational number is such that when you multiply it by 1/4 and add 2/5 to the product, you get 27/5. What is the number❓

10

15

20

25

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2021-08-16T05:05:43+00:00
2021-08-16T05:05:43+00:00 1 Answers
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## Answers ( )

Answer:Ncert solutions

Grade 8

Mathematics

Science

Chapters in NCERT Solutions – Mathematics , Class 8

Exercises in Linear Equations in One Variable

Question 13

Q13) A rational number is such that when you multiply it by \frac{5}{2}

2

5

and add \frac{2}{3}

3

2

to the product, you get -\frac{7}{12}−

12

7

. What is the number?

Solution

Transcript

Solution:

Let the rational number be x.

According to the question, \frac{5}{2}x+\frac{2}{3}=-\frac{7}{12}

2

5

x+

3

2

=−

12

7

\Rightarrow\ \frac{5}{2}x+\frac{2}{3}-\frac{2}{3}=-\frac{7}{12}-\frac{2}{3}⇒

2

5

x+

3

2

−

3

2

=−

12

7

−

3

2

[Subtracting \frac{2}{3}

3

2

from both sides]

\Rightarrow\ \frac{5x}{2}=\frac{-7-8}{12}⇒

2

5x

=

12

−7−8

\Rightarrow\ \frac{5x}{2}=\frac{-15}{12}⇒

2

5x

=

12

−15

\Rightarrow\ 5x\times12=-15\times2⇒ 5x×12=−15×2

\Rightarrow60x=-30⇒60x=−30

\Rightarrow\ \frac{60x}{60}=\frac{-30}{60}⇒

60

60x

=

60

−30

[Dividing both sides by 60]

\Rightarrow\ x=\ \frac{-1}{2}⇒ x=

2

−1

Hence, the rational number is \frac{-1}{2}

2

−1

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