Question

In my carpenter shop I make 3 legged stools and 4 legged chairs. I looked at my days output and counted 55 legs and 16 seats. How many stools and how many chairs did I complete that day.

Answer 1

$x-number\ of\ stools\\y-number\ of\ chairs\\\\ \left \{ {{y+x=16} \atop {3x+4y=55}} \right. \\\\From\ first\ equation:\\\\y=16-x\\\\Substract\ to\ second\ equation:\\\\3x+4(16-x)=55\\3x+64-4x=55\\3x-4x=55-64\\-x=-9\\x=9\\\\y=16-9=7\\\\ \left \{ {{y=7} \atop {x=9}} \right.$