Question 1156580
In a church choir the ratio of males to females is 2:3. 
<pre>
{{{M/F=2/3}}}

On one Sunday service ten male members were absent and six new female members joined the choir as guests for the day. 

Then the ratio was

{{{(M-10)/(F+6)}}}


If on this day the ratio of males to females was 1:3, 

{{{(M-10)/(F+6)=1/3}}}

how many regular choir members does the choir have?


Solve this system:

{{{system(M/F=2/3,(M-10)/(F+6)=1/3)}}}

Cross multiply both equations:

{{{system(M/F=2/3,(M-10)/(F+6)=1/3)}}}

{{{system(3M=2F,3(M-10)=1(F+6))}}}

{{{system(3M=2F,3M-30=F+6)}}}

{{{system(3M=2F,3M-36=F))}}}

From the second equation, substitute (3M-36) for F 
in the first equation, and solve to find M. Then substitute 
what you get for M in 3M-36=F to find F. 

I'll give you only the answer for the number of females, F=36.
You find the number of men and add them to find the number of
regular choir members.

Oh crap!  The other tutor already gave you the answer, darn it!

Edwin</pre>