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Linear Equations in One Variable
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05/08/2021 12:56 pm
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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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05/08/2021 12:57 pm
Let the numerator be x then denominator will be (x + 8)
According to the question,
(x + 17)/(x + 8 – 1) = 3/2
⇒ (x + 17)/(x + 7) = 3/2
⇒ 2(x + 17) = 3(x + 7)
⇒ 2x + 34 = 3x + 21
⇒ 34 – 21 = 3x – 2x
⇒ 13 = x
The rational number is x/(x + 8)
= 13/21