If a building contractor hires 5 day laborers and 2 concrete finishers, his payroll for the day is $1200. If he hire 1 day laborer and 4 concrete finishers, his daily cost is $924. Find the daily wage for each type of worker.
Well, it looks like the contractor is really playing with the numbers here. It's like a math puzzle that needs solving. Let's call the daily wage for a day laborer "D" and the daily wage for a concrete finisher "C."
So, if the contractor hires 5 day laborers and 2 concrete finishers, the equation would be 5D + 2C = 1200.
And if he hires 1 day laborer and 4 concrete finishers, the equation would be 1D + 4C = 924.
Now, let's put on our clown math hats and have some fun solving this puzzle.
Let's start by multiplying the second equation by 5 to get 5D + 20C = 4620.
Now, we can subtract the first equation from the second equation to eliminate the "D" term. This gives us:
(5D + 20C) - (5D + 2C) = 4620 - 1200.
Simplifying that, we get:
18C = 3420,
which means C (the daily wage for a concrete finisher) is 3420 divided by 18, or $190.
Now that we know the daily wage for a concrete finisher, let's substitute that back into one of the original equations. Let's use the first equation:
5D + 2C = 1200.
Substituting in the value we just found for C, we get:
5D + 2(190) = 1200.
Simplifying that, we have:
5D + 380 = 1200,
which means 5D = 1200 - 380, or 820.
So, the daily wage for a day laborer (D) is 820 divided by 5, or $164.
So, the daily wage for a day laborer is $164, and the daily wage for a concrete finisher is $190.
Voila! The math puzzle is solved, and the clown bot is happy to have provided the answer with a dash of humor.
Let's assume the daily wage for a day laborer is "x" and the daily wage for a concrete finisher is "y".
According to the given information, when the contractor hires 5 day laborers and 2 concrete finishers, the payroll for the day is $1200. This can be expressed as the equation:
5x + 2y = 1200.
Similarly, when the contractor hires 1 day laborer and 4 concrete finishers, the daily cost is $924. This can be expressed as another equation:
x + 4y = 924.
To find the daily wage for each type of worker, we need to solve this system of equations.
Step 1: Use the first equation to solve for x in terms of y.
5x = 1200 - 2y
x = (1200 - 2y)/5
Step 2: Substitute the value of x from the first equation into the second equation.
(1200 - 2y)/5 + 4y = 924
Step 3: Simplify and solve for y.
(1200 - 2y + 20y)/5 = 924
1200 + 18y = 924 * 5
1200 + 18y = 4620
18y = 4620 - 1200
18y = 3420
y = 3420/18
y = 190
Step 4: Substitute the value of y back into the first equation to find x.
x = (1200 - 2*190)/5
x = (1200 - 380)/5
x = 820/5
x = 164
Therefore, the daily wage for a day laborer is $164 and the daily wage for a concrete finisher is $190.
To find the daily wage for each type of worker, we can set up a system of equations based on the given information.
Let's denote the daily wage for a day laborer as D and the daily wage for a concrete finisher as C.
Based on the first scenario, where the building contractor hires 5 day laborers and 2 concrete finishers, the total payroll for the day is $1200. This can be expressed as the equation:
5D + 2C = 1200 ----(1)
Similarly, in the second scenario, where the contractor hires 1 day laborer and 4 concrete finishers, the total cost for the day is $924. This can be expressed as:
1D + 4C = 924 ----(2)
Now, we can solve this system of equations to find the values of D and C.
To do this, we can use the method of substitution. Rearrange equation (1) to solve for D:
D = (1200 - 2C) / 5 ----(3)
Substitute equation (3) into equation (2):
(1200 - 2C) / 5 + 4C = 924
Multiply both sides by 5 to remove the denominator:
1200 - 2C + 20C = 924 * 5
1200 + 18C = 4620
18C = 4620 - 1200
18C = 3420
Divide both sides by 18 to solve for C:
C = 3420 / 18
C = 190
Now, substitute the value of C back into equation (3) to find the value of D:
D = (1200 - 2 * 190) / 5
D = (1200 - 380) / 5
D = 820 / 5
D = 164
Therefore, the daily wage for each type of worker is $164 for a day laborer and $190 for a concrete finisher.
set up system of equations:
x = wage of laborers
y = wage of concrete finishers
5x+2y = 1200
x+4y = 924
Now solve the system of equations:
from the second equation, isolating x we get:
x = 924 - 4y
now plug that into the first equation:
5(924-4y)+2y=1200
y = 190
now plug y back into one of the equations to find x:
x+4(190) = 924
x = 164
daily wage of laborer = 164
daily wage of concrete finishers = 190