The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
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Let the numerator of the rational number be x.
So as per the given condition, the denominator will be x + 8.
The rational number will be \(\frac{x}{x+8}\)
According to the given condition,
\(\frac{x+17}{x+8-1} = \frac{3}{2}\)
\(\frac{x+17}{x+7} = \frac{3}{2}\)
3(x + 7) = 2(x + 17)
3x + 21 = 2x + 34
3x – 2x + 21 – 34 = 0
x – 13 = 0
x = 13
The rational number will be
= \(\frac{x}{x+8}\)
= \(\frac{13}{13+8}\)
Rational number = 13/21
Answer:
Let the numerator of the rational number be x.
So as per the given condition, the denominator will be x + 8.
The rational number will be \(\frac{x}{x+8}\)
According to the given condition,
\(\frac{x+17}{x+8-1} = \frac{3}{2}\)
\(\frac{x+17}{x+7} = \frac{3}{2}\)
3(x + 7) = 2(x + 17)
3x + 21 = 2x + 34
3x – 2x + 21 – 34 = 0
x – 13 = 0
x = 13
The rational number will be
= \(\frac{x}{x+8}\)
= \(\frac{13}{13+8}\)
Rational number = 13/21
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