Question

What is the value of k in the equation 4/9(k+4/7)=3 1/3 ?

Answer 1

The equation given in the question has one unknown variable and so the value of k can definitely be found.
4/9(k + 4/7) = 3 1/3
4/9[(7k + 4)] = 10/3
4/(63k + 36) = 10/3
4 * 3 = 10 * (63k + 36)
12 = 630k + 360
12 - 360 = 630k
- 348 = 630k
Reversing both sides we get
630k = - 348
k = - 348/630
  = - 174/315
  = - 58/105
So the value of K comes out to be - 58/105 and it is not possible to simplify it further.

Answer 2

$\dfrac{4}{9}\left(k+\dfrac{4}{7}\right)=3\dfrac{1}{3}\\ \dfrac{4}{9}\left(k+\dfrac{4}{7}\right)=\dfrac{10}{3}\\ k+\dfrac{4}{7}=\dfrac{10}{3}\cdot\dfrac{9}{4}\\ k+\dfrac{4}{7}=\dfrac{15}{2}\\ k=\dfrac{105}{14}-\dfrac{8}{14}\\ k=\dfrac{97}{14}$