Question

What is the value of k in the equation 3/2(k+2/5)=2 1/3 ?

Answer 1

`(3)/(2)\left(k+(2)/(5)\right)=2(1)/(3)\\ (3)/(2)\left(k+(2)/(5)\right)=(7)/(3)\\\ k+(2)/(5)=(7)/(3)\cdot(2)/(3)\\ k+(2)/(5)=(14)/(9)\\ k=(14)/(9)-(2)/(5)\\ k=(70)/(45)-(18)/(45)\\ k=(52)/(45)`

Answer 2

Let us first write down the given equation and then start simplifying.
3/2(k + 2/5) = 2 1/3
3/(2k + 4/5) = 7/3
3/[(10k + 4)/5] = 7/3
3 * 3 = 7[(10k +4)/5]
9 = (70k + 28)/5
9 * 5 = 70k + 28
45 = 70k + 28
45 - 28 = 70k
17= 70k
Reversing both sides we get
70k = 17
k = 17/70
So the value of k comes out to be 17/70 and it is impossible to simplify it further.