He sum of the numerator and the denominator of the certain fraction is equal to 4,140. when the fraction was reduced, the result was 7 13. what was the original fraction?

1449/2691

Step-by-step explanation:

Let the fraction be x/y. Then, we have two conditions:

(1) x + y = 4140

(2) x/y = 7/13

(3) 13x = 7y Multiplied each side by the lcd (13y)

(4) y = 4140 - x Subtracted x from each side of (1)

13x = 7 (4140 - x) Substituted (4) into (3)

13x = 28 980 - 7x Distributed the 7

20x = 28 980 Added 7x to each side

(5) x = 1449

1449 + y = 4140 Substituted (5) into (1)

y = 2691 Subtracted 1449 from each side

The original fraction was 1449/2691.

Check:

(1) 1449 + 2691 = 4140 (2) 1449/2691 = 7/13

4140 = 4140 7/13 = 7/13

OK.