Question

the numerator of a fraction is 3 less than THE denominator . if the numerator and denominator are both increased by 2 the new fraction become 6/7 find the orignal number

Answer 1

Hi ,

Let denominator = x ,

numerator = ( x - 3 )

Original number = ( x - 3 )/x ---( 1 )

If the numerator and denominator are

both increased by 2 the new fraction = 6/7

( x - 3 + 2 )/ ( x + 2 ) = 6/7

( x - 1 )/( x + 2 ) = 6/7

7( x - 1 ) = 6( x + 2 )

7x - 7 = 6x + 12

7x - 6x = 12 + 7

x = 19

Therefore ,

Original number = ( x - 3 )/x

= ( 19 - 3 )/19

= 16/19

I hope this helps you.

: )

Answer 2

Let,
denominator be x
numerator be x-3

======================

According to the question

$\frac{x - 3 + 2}{x + 2} = \frac{6}{7} \\ \frac{x - 1}{x + 2} = \frac{6}{7} \\ \\ 7(x - 1) = 6(x + 2) \\ \\ 7x - 7 = 6x + 12 \\ \\ 7x - 6x = 12 + 7 \\ \\ x = 19 \\ \\ \\ \\ fraction \: is \: \frac{x - 3}{x} = \frac{19 - 3}{19} = \frac{16}{19}$


Original fraction = 16/19



I hope this will help you


-by ABHAY