Question

The numerator of a rational number is less than its denominator by 3. If the numerator becomes 3 times and denominator is increased by 20, the new number becomes 1/8.Find the original number.
(3 Points)​

Answer 1

Question:

• The numerator of a rational number is less than its denominator by 3. If the numerator becomes 3 times and denominator is increased by 20, the new number becomes 1/8.Find the original number.

❍ Let the denominator of the fraction be x respectively. Then, it's numerator becomes

(x - 3).

By the question  :

• If the numerator becomes 3 times and denominator is increased by 20, the new number becomes 1/8.Find the original number.

Therefore,

$\longrightarrow \frac{numerator \times 3}{denominator + 20} = \frac{1}{8} \\ \\ \longrightarrow \frac{3 \times( x - 3)}{x + 20} = \frac{1}{8} \\ \\ \longrightarrow \frac{3x - 9}{x + 20} = \frac{1}{8} \\ \\ \longrightarrow 8(3x - 9) = 1(x + 20) \\ \\ \longrightarrow 24x - 72 = x + 20 \\ \\ \longrightarrow 24x - x = 20 + 72 \\ \\ \longrightarrow 23x = 92 \\ \\ \longrightarrow x = \frac{92}{23} \\ \\ \longrightarrow x= 4$

Hence,

• Denominator of the fraction is x = 4.

• Numerator of the fraction is (x -3 ) = ( 4 - 3 ) =  1.

∴

Hence,  the required rational number is 1/4.

Answer 2

Answer:

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