SOLUTION: the numerator of a fraction is 3 less than the denominator. when both the numerator and denominator are increased by 4, the fraction is increased by 12/77. find the original fracti

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: the numerator of a fraction is 3 less than the denominator. when both the numerator and denominator are increased by 4, the fraction is increased by 12/77. find the original fracti      Log On


   

Question 186856: the numerator of a fraction is 3 less than the denominator. when both the numerator and denominator are increased by 4, the fraction is increased by 12/77. find the original fraction.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let d be the denominator
n = d-3
Told
%28d-3%2B4%29%2F%28d%2B4%29+=+%28%28d-3%29%2Fd%29%2B+12%2F177
%28d%2B1%29%2F%28d%2B4%29+=+%28%28d-3%29%2Fd%29%2B+12%2F177
%28%28d%2B1%29%2A177d%29%2F%28d%2B4%29+=+177%28d-3%29%2B+12d
177d%5E2+%2B+177d+=+%28189d+-+531%29%28d%2B4%29
177d%5E2+%2B+177d+=+189d%5E2+-+531d+%2B+756d+-+2124
0+=+12d%5E2+%2B+48d+-+2124
0+=+d%5E2+%2B+4d+-+177
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-177+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A-177=724.

Discriminant d=724 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+724+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+724+%29%29%2F2%5C1+=+11.4536240470737
x%5B2%5D+=+%28-%284%29-sqrt%28+724+%29%29%2F2%5C1+=+-15.4536240470737

Quadratic expression 1x%5E2%2B4x%2B-177 can be factored:
1x%5E2%2B4x%2B-177+=+1%28x-11.4536240470737%29%2A%28x--15.4536240470737%29
Again, the answer is: 11.4536240470737, -15.4536240470737. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-177+%29


d = 11.45
Original fraction = 8.45/11.45