SOLUTION: In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is 2/3. Find the original numbe

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is 2/3. Find the original numbe      Log On


   

Question 921311: In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is 2/3. Find the original number.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

start with a%2Fb
twice the numerator (2a) is 2 more than the denominator ( b):
2a=b%2B2 =>a=b%2F2%2B1
the new fraction is a%2Fb=%28b%2F2%2B1%29%2Fb
3 is added to each
%28%28b%2F2%2B1%29%2B3%29%2F%28b%2B3%29 and it is equal to 2%2F3
%28%28b%2F2%2B1%29%2B3%29%2F%28b%2B3%29+=2%2F3 .........solve for b
%28b%2F2%2B4%29%2F%28b%2B3%29+=2%2F3+
3%28b%2F2%2B4%29+=2%28b%2B3%29
3b%2F2%2B12+=2b%2B6
12-6+=2b-3b%2F2
6=4b%2F2-3b%2F2
6+=b%2F2
6%2A2+=b
12=b
=>a=b%2F2%2B1 => a=12%2F2%2B1 => a=6%2B1=>a=7
original fraction is: a%2Fb=7%2F12