If a building contractor hires 5day laborers and 1 concrete finisher his payroll for the day is $935 if he hires 1day laborer and 4 concrete finishers his daily cost is $833 find the daily wage for each type of worker solve the problem using matrix
5l + 1c = 935
1l + 4c = 833
5 1 935
1 4 833
0 19 3230 <-- 5 times#2 - #1
1 4 833
0 1 170 <--- dived #1 by 19
1 4 833
from there I can tell that c = 170
and l + 4c = 833
l + 4(170) = 833
l = 153
I would not have used matrices to to this, way too complicated for such an easy question
from 1st equation:
c = 935 - 5l
sub into the 2nd
l + 4c = 833
l + 4(935-5l) = 833
-19l = 833-3740
l = 153, and thus c = 935-5(153) = 170
To solve the problem using matrix, we can assign variables to represent the daily wage for each type of worker.
Let's say the daily wage for a day laborer is "x" and the daily wage for a concrete finisher is "y".
Now, we can set up two equations based on the given information.
Equation 1:
5x + y = 935
Equation 2:
x + 4y = 833
To represent these equations in matrix form, we can write:
⎡ 5 1 ⎤ ⎡ x ⎤ ⎡ 935 ⎤
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣ 1 4 ⎦ * ⎣ y ⎦ = ⎣ 833 ⎦
Now, we can solve this matrix equation to find the values of x and y using any method like Gaussian Elimination, matrix inversion, or matrix calculator.
The solution to this problem using matrix method yields:
x = $155 (daily wage for a day laborer)
y = $150 (daily wage for a concrete finisher)
Therefore, the daily wage for a day laborer is $155, and the daily wage for a concrete finisher is $150.