Question

The numerator of a rational number is 3 less than the denominator. If the
numerator is increased by 8 and the denominator increased by 14, we get the
same number. Find the number.
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Answer 1

Your Answer:

Given:-

• The numerator of a rational number is 3 less than the denominator
• If the  numerator is increased by 8 and the denominator increased by 14, we get the  same number

To Find:-

• The number

Solution:-

Let the numerator be 'x' and denominator be 'y'

So, the number is x/y

So, ATQ

$\tt \dfrac{x+8}{y-14} = \dfrac{x}{y} \\\\ \tt Now, \ solving \ the \ Equations \\\\ \tt \Rightarrow y(x+8) = x(y-14) \\\\ \tt \Rightarrow xy + 8y = xy - 14x \\\\ \tt \Rightarrow \cancel{xy} + 8y = \cancel{xy} - 14x \\\\ \tt \Rightarrow 8y = 14x \\\\ \tt \Rightarrow 4y = 7x \rightarrow \rightarrow \rightarrow (1)$

Also,

x + 3 = y -------------> (2)

putting value of y in equation one

$\tt4(x+3) = 7x \\\\ \tt \Rightarrow 4x + 12 = 7x \\\\ \tt \Rightarrow 12 = 3x \\\\ \tt \Rightarrow \dfrac{12}{3} = x \\\\ \tt \Rightarrow 4 = x$

Putting the value of x in eq 2

$\tt y = x+3\\\\ \Rightarrow y = 4 + 3 \\\\ \tt \Rightarrow y = 7$

So, the number is x/y = 4/7

Answer 2

Answer:

Step-by-step explanation: