SOLUTION: thirty buliding operatives employed on a construction site work a 37 hour week. if the 30 operatives comprise tradesmen earning £4.75/ hour and labourers earning £4.25/ hour, how

Algebra ->  Matrices-and-determiminant -> SOLUTION: thirty buliding operatives employed on a construction site work a 37 hour week. if the 30 operatives comprise tradesmen earning £4.75/ hour and labourers earning £4.25/ hour, how       Log On


   

Question 557023: thirty buliding operatives employed on a construction site work a 37 hour week. if the 30 operatives comprise tradesmen earning £4.75/ hour and labourers earning £4.25/ hour, how many tradesmen and how many labourers are there if the weekly bill is £5124.50. using matrices?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of tradesmen and y be the number of laborers.
x%2By=30 and
4.75x%2B4.25y=5124.50%2F37=138.50 ---> 19x%2B17y=554 (multiplying both sides times 4 to get rid of decimals)
%28matrix%282%2C2%2C1%2C1%2C19%2C17%29%29%28matrix%282%2C1%2Cx%2Cy%29%29=%28matrix%282%2C1%2C30%2C554%29%29
Now you have your matrices:
A = %28matrix%282%2C2%2C1%2C1%2C19%2C17%29%29
X = %28matrix%282%2C1%2Cx%2Cy%29%29 , and
B = %28matrix%282%2C1%2C30%2C554%29%29
The equation with matrices is
AX=B
Now you have to find the inverse matrix A%5E-1 and calculate
X=A%5E-1B
Whichever way you were taught to calculate it
A%5E-1 = %28matrix%282%2C2%2C-17%2F2%2C1%2F2%2C19%2F2%2C-1%29%29 and
X=%28matrix%282%2C2%2C-17%2F2%2C1%2F2%2C19%2F2%2C-1%29%29%28matrix%282%2C1%2C30%2C554%29%29 = %28matrix%282%2C1%2C22%2C8%29%29
X = %28matrix%282%2C1%2Cx%2Cy%29%29 = %28matrix%282%2C1%2C22%2C8%29%29
So the number of tradesmen is x=22 , and
the number of laborers is y=8 .