Question
If a building contractor hires 5 day laborers and 2 concrete finishers, his payroll for the day is $1285. If he hires 1 day laborer and 5 concrete finishers, his daily cost is $1177. Find the daily wage for each type of worker. Solve the problem using matrices.
Answers
you need to solve the system
5d+2c = 1285
1d+5c = 1177
So, you have AX = B,
(5 2) (d) = (1285)
(1 5) (c) = (1177)
A<sup><sup>-1</sup></sup> =
(5/23 -2/23)
(-1/23 5/23)
X = A<sup><sup>-1</sup></sup> * B, so
(d) = 200
(c) = 177
5d+2c = 1285
1d+5c = 1177
So, you have AX = B,
(5 2) (d) = (1285)
(1 5) (c) = (1177)
A<sup><sup>-1</sup></sup> =
(5/23 -2/23)
(-1/23 5/23)
X = A<sup><sup>-1</sup></sup> * B, so
(d) = 200
(c) = 177