The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, then the new number becomes
3
2
. Find the original number.
Answers
Answer:
Solution
Transcript
Solution:
Let the numerator of a rational number be x then the denominator is x+8.
Therefore, Rational number = \frac{x}{x+8}
x+8
x
According to the question,
\frac{x+17}{x+8-1}=\frac{3}{2}
x+8−1
x+17
=
2
3
\Rightarrow\ \frac{x+17}{x+7}=\frac{3}{2}⇒
x+7
x+17
=
2
3
\Rightarrow\ 2\left(x+17\right)=3\left(x+7\right)⇒ 2(x+17)=3(x+7)
\Rightarrow\ 2x+34=3x+21⇒ 2x+34=3x+21
\Rightarrow\ 2x-3x=21-34⇒ 2x−3x=21−34
\Rightarrow\ -x=-13⇒ −x=−13
\Rightarrow\ x=13⇒ x=13
Hence, the required rational number
=\ \frac{x}{x+8}=\frac{13}{13+8}=\frac{13}{21}=
x+8
x
=
13+8
13
=
21
13
Answer:
According to the question,
Original number = x/(x + 3)
New number = (x + 7)/(x + 3 - 1)
⇒ (x + 7)/(x + 2) = 3/2.
⇒ 2(x + 7) = 3(x + 2)
⇒ 2x + 14 = 3x + 6
⇒ 3x - 2x = 14 - 6
⇒ x = 8.
Original number = x/(x + 3)
= 8/(8 + 3)
= 8/11.
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