If a building contractor hires 5 day laborers and 2 concrete finishers, his payroll for the day is $1200. If he hires i day laborer and 4 concrete finishers, his daily cost is $924. Find the daily wage for each type of worker.
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To find the daily wage for day laborers and concrete finishers, let's denote the daily wage for day laborers as "x" dollars and the daily wage for concrete finishers as "y" dollars.
From the given information, we can form two equations:
Equation 1: 5x + 2y = 1200 (when 5 day laborers and 2 concrete finishers are hired)
Equation 2: x + 4y = 924 (when 1 day laborer and 4 concrete finishers are hired)
We will solve this system of equations to find the values of x and y.
Multiplying Equation 2 by 5, we get:
5x + 20y = 4620
Now, subtract Equation 1 from this equation:
5x + 20y - (5x + 2y) = 4620 - 1200
18y = 3420
Dividing both sides by 18:
y = 190
Substituting the value of y back into Equation 2:
x + 4(190) = 924
x + 760 = 924
x = 924 - 760
x = 164
Therefore, the daily wage for each day laborer is $164, and the daily wage for each concrete finisher is $190.