The numerator of a rational number is 3 less than the denominator. If the numerator is increased by 8 and the denominator increased by

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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Evelyn 3 weeks 2021-09-04T17:00:21+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-04T17:02:08+00:00

    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

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