Question

PLEASE ANSWER!!!! WILL GIVE 20 POINTS!!!!

Answer 1

Original fraction was $\dfrac{7\cdot k}{13\cdot k}$ where $k$ is a reduced common factor. We know that:

$7k+13k=4140\\\\20k=4140\qquad|:20\\\\\boxed{k=207}$

so original fraction:

$\dfrac{7\cdot k}{13\cdot k}=\dfrac{7\cdot 207}{13\cdot 207}=\boxed{\dfrac{1449}{2691}}$

Answer 2

Let's named variables n-numerator and d-denumerator

n+d=4,140 ∧  n/d=7/13 => n=(7/13)d

Then we replace n and get  (7/13)d+d=4,140 => (7/13)d +(13/13)d = 4,140

(20/13)d = 4,140 => d= (4,140 * 130) /20 = 2,691

n= (7/13) * 2,691 = 1,449

The original fraction is 1,449/2,691

Good luck!!!