SOLUTION: If a team consists 20 members in which 20% are mathematician then how many member should they hire sothat the ratio would become 10/11.

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Question 389435: If a team consists 20 members in which 20% are mathematician then how many member should they hire sothat the ratio would become 10/11.
Answer by gwendolyn(128) About Me  (Show Source):
You can put this solution on YOUR website!
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:
%284+%2B+x%29%2F%2820+%2B+x%29+=+10%2F11
Multiply both sides by 11:
11%2A%284+%2B+x%29%2F%2820+%2B+x%29+=+%2810%2A11%29%2F11
Distribute the 11 on the left and "cross out" 11/11 on the right:
%2844+%2B+11x%29%2F%2820+%2B+x%29+=+10
Multiply both sides by (20 + x)
%2844+%2B+11x%29%2A%2820+%2B+x%29%2F%2820+%2B+x%29+=+10%2A%2820+%2B+x%29
"Cross out" (20 + x)/(20 + x) on the left and distribute the ten on the right:
44+%2B+11x+=+200+%2B+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.