Eight-ninths of a bunch of marbles remain on a table. The square root of half the total number of marbles have rolled away. Also, the two children who are playing with the marbles each hold one marble. Find the total number of marbles in the bunch.

To find the total number of marbles in the bunch, we need to work backwards step by step using the information given.

Let's assume the total number of marbles in the bunch is "x".

First, we know that eight-ninths of the marbles remain on the table. This means (8/9)x marbles remain on the table.

Next, we're told that the square root of half the total number of marbles have rolled away. In other words, the square root of (1/2)x marbles have rolled away.

So, the number of marbles remaining on the table is (8/9)x - √((1/2)x).

We're also told that each child holds one marble. Since there are two children, we need to subtract 2 marbles from the number of marbles remaining on the table.

Therefore, the final equation is:

(8/9)x - √((1/2)x) - 2 = 0

Now, we can solve this equation to find the value of x, which represents the total number of marbles in the bunch.