Question

The denominator of a number is greater than its numerator by 8 if the numerator increases by 17 and denominator decreases by 1 we get 3/2 fund the rational number

Answer 1

Answer :

Given :

• The denominator of a number is greater than its numerator by 8
• The numerator increases by 17 and denominator decreases by 1 we get $\dfrac{3}{2}$

Find :

• Find the rational number.

Step By Step Explanation :

Let,

• The numerator be x
• The denominator be x + 8

According to the question :

= ${\sf{\dfrac{x+17}{(x+8)-1} = \dfrac{3}{2}}}$

= ${\sf{2(x + 17) = 3(x+8)-1}}$

= ${\sf{2x + 34= 3x+24 -1}}$

= ${\sf{2x - 3x= 23-34}}$

= ${\sf{-x= -11}}$

= ${\sf{x= 11}}$

Now, put x = 11 for obtaining the fraction.

= ${\sf{\dfrac{x}{(x+8)}}}$

= ${\sf{\dfrac{9}{(9+8)}}}$

= ${\sf{\dfrac{9}{17}}}$

•°• The rational number is 9/17 .

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