Two fractions have denominators 4 and 6. their sum is 19/12
if the numerators are switched their sum is 7/4
determine the value of the numerators.

The value of numerators are 3 and 5

Solution:

Let the numerators of two fractions be x and y

Two fractions have denominators 4 and 6. Their sum is 19/12

Therefore,

Cross multiply L.H.S to get simplified

If the numerators are switched their sum is 7/4

Therefore,

On simplification, we get

Solve eqn 1 and eqn 2

Multiply eqn 1 by 4

24x + 16y = 152 --------- eqn 3

Multiply eqn 2 by 6

24x + 36y = 252 ---------- eqn 4

Subtract eqn 3 from eqn 4

24x + 36y = 252

24x + 16y = 152

( - ) -------------------

20y = 100

Substitute y = 5 in eqn 1

6x + 4(5) = 38

6x = 38 - 20

6x = 18

Thus the value of numerators are 3 and 5

360/29

step-by-step explanation: