Question

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.​

Answer 1

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,

`(x)/(4) + (y)/(6) = (19)/(12)`

Cross multiply L.H.S to get simplified

`(6x+4y)/(24) = (19)/(12)\\\\6x + 4y = 38 ------- eqn 1`

If the numerators are switched their sum is 7/4

Therefore,

`(y)/(4) + (x)/(6) = (7)/(4)`

On simplification, we get

`(6y + 4x)/(24) = (7)/(4)\\\\4x + 6y = 42 -------- eqn 2`

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

y = 5

Substitute y = 5 in eqn 1

6x + 4(5) = 38

6x = 38 - 20

6x = 18

x = 3

Thus the value of numerators are 3 and 5