Suppose 1 boy alone can can do 1 job in b days.

Then 1 boy's work rate is 1 job per b days or  or 

Then 12 boys' work rate is 12 times  or 

and 8 boys' work rate is 8 times  or 

Suppose 1 man alone can can do 1 job in m days.

Then 1 man's work rate is 1 job per m days or  or 

Then 8 men's work rate is 8 times  or 

and 6 men's work rate is 6 times  or 

So the combined work rate of 12 boys and 8 men is 1 job per 5 days or  or 

So we get one equation from




>>8 boys and 6 men can finish it in 7 days<<


So the combined work rate of 8 boys and 6 men is 1 job per 7 days or  or 



So we get the other equation from







 



So we have the system of equations







IMPORTANT:  DO NOT CLEAR OF FRACTIONS:



To eliminate the terms in m, multiply the first equation 

through by 3, and multiply the second equation through

by -4:





 

Adding those equations term by term gives







NOW we can clear of fractions.  Multiply both sides

by the LCD of 35b











So each boy will take 140 days.



Substitute 140 for b in











Multiply both sides by 10m









So each man will take 80 days.



Edwin