Question 389435
First let's figure out how many mathematicians are already on the team:

20 members times 20% is the same as:

20*.2 = 4

So, there are already 4 mathematicians on the team.
We need to add x more mathematicians.
Whenever we add x mathematicians, we add x to the original 4 mathematicians, 
and we also add x to the number of total team members. 
We need to find the value for x which provides a ratio of 10/11:

{{{(4 + x)/(20 + x) = 10/11}}}
Multiply both sides by 11:
{{{11*(4 + x)/(20 + x) = (10*11)/11}}}
Distribute the 11 on the left and "cross out" 11/11 on the right:
{{{(44 + 11x)/(20 + x) = 10}}}
Multiply both sides by (20 + x)
{{{(44 + 11x)*(20 + x)/(20 + x) = 10*(20 + x)}}}
"Cross out" (20 + x)/(20 + x) on the left and distribute the ten on the right:
{{{44 + 11x = 200 + 10x}}}
Subtract 10x and 44 from both sides to isolate the variable:
44 + 11x - 44 - 10x = 200 + 10x - 44 - 10x
x = 200 - 44
x = 156

So, we need to add 156 mathemeticians to the team.