SOLUTION: this is the word problem.thanks the value of a fraction is 2/3.if the numerator is increased by 1 and the denominator is reduced by 1,the value of the fraction becomes 1.find the

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: this is the word problem.thanks the value of a fraction is 2/3.if the numerator is increased by 1 and the denominator is reduced by 1,the value of the fraction becomes 1.find the       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 325319: this is the word problem.thanks
the value of a fraction is 2/3.if the numerator is increased by 1 and the denominator is reduced by 1,the value of the fraction becomes 1.find the original.
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
if the numerator is increased by 1 and the denominator is reduced by 1,the value of the fraction becomes 1.find the original

Let N = the numerator
Let D = the denominator
Then N%2FD = the fraction


system%28N%2FD=2%2F3%2C%28N%2B1%29%2F%28D-1%29=1%29

system%283N=2D%2CN%2B1=D-1%29

system%283N=2D%2CN=D-2%29

Use substitution, replace N in the first by D-2 from the second

3N=2D

3%28D-2%29=2D

3D-6=2D

D=6

Substitute that in

N=D-2%29

N=6-2%29

N=4

So the fraction is 4%2F6

Checking:

Adding one to the numerator and subtracting one from the
denominator gives %284%2B1%29%2F%286-1%29=5%2F5=1

Edwin