Question

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

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,

$\frac{x}{4} + \frac{y}{6} = \frac{19}{12}$

Cross multiply L.H.S to get simplified

$\frac{6x+4y}{24} = \frac{19}{12}\\\\6x + 4y = 38 ------- eqn 1$

If the numerators are switched their sum is 7/4

Therefore,

$\frac{y}{4} + \frac{x}{6} = \frac{7}{4}$

On simplification, we get

$\frac{6y + 4x}{24} = \frac{7}{4}\\\\4x + 6y = 42 -------- eqn 2$

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