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❓
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2021-08-16T05:05:43+00:00
2021-08-16T05:05:43+00:00 1 Answers
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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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