document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #275964 by gwendolyn(128) $\"\"$ $\"About$

You can put this solution on YOUR website!
First let's figure out how many mathematicians are already on the team:\r
\n" ); document.write( "\n" ); document.write( "20 members times 20% is the same as:\r
\n" ); document.write( "\n" ); document.write( "20*.2 = 4\r
\n" ); document.write( "\n" ); document.write( "So, there are already 4 mathematicians on the team.
\n" ); document.write( "We need to add x more mathematicians.
\n" ); document.write( "Whenever we add x mathematicians, we add x to the original 4 mathematicians,
\n" ); document.write( "and we also add x to the number of total team members.
\n" ); document.write( "We need to find the value for x which provides a ratio of 10/11:\r
\n" ); document.write( "\n" ); document.write( " $\"%284+%2B+x%29%2F%2820+%2B+x%29+=+10%2F11\"$
\n" ); document.write( "Multiply both sides by 11:
\n" ); document.write( " $\"11%2A%284+%2B+x%29%2F%2820+%2B+x%29+=+%2810%2A11%29%2F11\"$
\n" ); document.write( "Distribute the 11 on the left and \"cross out\" 11/11 on the right:
\n" ); document.write( " $\"%2844+%2B+11x%29%2F%2820+%2B+x%29+=+10\"$
\n" ); document.write( "Multiply both sides by (20 + x)
\n" ); document.write( " $\"%2844+%2B+11x%29%2A%2820+%2B+x%29%2F%2820+%2B+x%29+=+10%2A%2820+%2B+x%29\"$
\n" ); document.write( "\"Cross out\" (20 + x)/(20 + x) on the left and distribute the ten on the right:
\n" ); document.write( " $\"44+%2B+11x+=+200+%2B+10x\"$
\n" ); document.write( "Subtract 10x and 44 from both sides to isolate the variable:
\n" ); document.write( "44 + 11x - 44 - 10x = 200 + 10x - 44 - 10x
\n" ); document.write( "x = 200 - 44
\n" ); document.write( "x = 156\r
\n" ); document.write( "\n" ); document.write( "So, we need to add 156 mathemeticians to the team. \n" ); document.write( "

\n" );