In a fraction, if 1 is added to both the numerator at the denominator, the fraction becomes 1/2. If numerator is subtracted from the denominator, the fraction becomes 3/4. Find the fraction. Pick one:
A) 3/7  B) 4/7  C) 5/7  D) 6/7  E) 8/7
Let fraction be a/b, where a and b are integers.   "If 1 is added to both the numerator and denominator, the fraction becomes 1/2"   (a+1)/(b+1) = 1/2   2(a+1)  ( +1)/( +1)= 
<gadget id="calculator"> ( +1)/( +1)</gadget>
<output>1</output>
1/2   2(a+1)= b+1   2a + 2 = b + 1   2a - b = -1   "If numerator is subtracted from the denominator, the fraction becomes 3/4"   a/(b-a) = 3/4   4a = 3(b-a)   4a = 3b - 3a   4a + 3a - 3b = 0   7a - 3b = 0   Now we just need to solve system of linear equations:   2a - b = -1 . . . [1]   7a - 3b = 0 . . . [2]   From [1], we get:   b = 2a + 1   Substituting in this value of b into [2], we get   7a - 3(2a+1) = 0   7a - 6a - 3 = 0   a - 3 = 0   a = 3   b = 2(3)+1   b = 7   So original fraction is a/b = 3/7   3/7NSWER:3/7
<result>A</result>
In a fraction, if 1 is added to both the numerator at the denominator, the fraction becomes 1/2. If numerator is subtracted from the denominator, the fraction becomes 3/4. Find the fraction.