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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Elliana 1 month 2021-08-16T05:05:43+00:00 1 Answers 0 views 0

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    0
    2021-08-16T05:07:39+00:00

    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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