Question 914508
the numerator of a fraction is 18 less than the denominator. if 1 is added to the numerator and subtracted from the denominator,the resulting fraction is 2/3. find the fraction

N= D-18

{{{(N+1)/(D-1) = 2/3}}}

substitute N

{{{((D-18)+1)/(D-1) = 2/3}}}



{{{(D-17)/(D-1) = 2/3}}}


3(D-17)=2(D-1)

3D-51=2D-2

D=49

N=D-18

N=49-18

N=31

The fraction 31/49




problem 2
the sum of the digits of a two-digit number is 13. if the digits are reversed, the resulting number is 9 less than the original number. what is the original number?

x+y=13.................(1)

10y+x=10x+y-9

9y-9x=-9

y-x=-1............(2)

add (1) & (2)

2y=12
y=6

x+y=13

x=7

Number = 76