Question 557023
Let {{{x}}} be the number of tradesmen and {{{y}}} be the number of laborers.
{{{x+y=30}}} and
{{{4.75x+4.25y=5124.50/37=138.50}}} ---> {{{19x+17y=554}}} (multiplying both sides times 4 to get rid of decimals)
{{{(matrix(2,2,1,1,19,17))}}}{{{(matrix(2,1,x,y))}}}={{{(matrix(2,1,30,554))}}}
Now you have your matrices:
{{{A}}} = {{{(matrix(2,2,1,1,19,17))}}}
{{{X}}} = {{{(matrix(2,1,x,y))}}} , and
{{{B}}} = {{{(matrix(2,1,30,554))}}}
The equation with matrices is
{{{AX=B}}}
Now you have to find the inverse matrix {{{A^-1}}} and calculate
{{{X}}}={{{A^-1B}}}
Whichever way you were taught to calculate it
{{{A^-1}}} = {{{(matrix(2,2,-17/2,1/2,19/2,-1))}}} and
{{{X}}}={{{(matrix(2,2,-17/2,1/2,19/2,-1))}}}{{{(matrix(2,1,30,554))}}} = {{{(matrix(2,1,22,8))}}}
{{{X}}} = {{{(matrix(2,1,x,y))}}} = {{{(matrix(2,1,22,8))}}}
So the number of tradesmen is {{{x=22}}} , and
the number of laborers is {{{y=8}}} .