A man will pay RM 46000 to renovate an office . If the construction materials cost 25% more and the labour costs 30% more , he will need to pay RM 58540. Find the original cost of the construction meterial and the cost of labour .(Used equation)
The cost of renovating the office consists of construction materials and labour costs.
So we let x and y be cost of construction materials and labour respectively.
This means x + y = 46000
If the materials are 25% more and labour 30% more, renovation costs are RM58540.
So our second equation is
125/100x + 130/100y = 58540
Now we have 2 equations so we can solve for both unknowns. :)
sasadad
Let's assume the original cost of construction materials is M, and the original cost of labor is L.
According to the given information, the construction materials cost 25% more, so the new cost of construction materials is 1.25M.
Similarly, the labor costs 30% more, so the new cost of labor is 1.3L.
From the given information, we can form the following equation:
1.25M + 1.3L = 58540 .......(Equation 1)
We are also given that the man will pay RM 46000 for the renovation, which means the total cost before the increase in material and labor costs is RM 46000. Therefore, we can form a second equation:
M + L = 46000 .......(Equation 2)
Now, we can solve the system of equations using the substitution method.
From Equation 2, we can express L in terms of M:
L = 46000 - M
Substituting this value of L into Equation 1:
1.25M + 1.3(46000 - M) = 58540
Simplifying the equation:
1.25M + 59800 - 1.3M = 58540
0.05M = 1250
M = 1250 / 0.05
M = 25000
So, the original cost of construction materials is RM 25000.
Substituting this value of M back into Equation 2:
25000 + L = 46000
L = 46000 - 25000
L = 21000
Therefore, the cost of labor is RM 21000.
To find the original cost of the construction materials and the cost of labor, we can set up a system of equations based on the given information.
Let's assume the original cost of the construction materials is x and the cost of labor is y.
According to the problem, when the construction materials cost 25% more and the labor costs 30% more, the total cost is RM 58540. We can represent this information in the following equation:
x + 0.25x + y + 0.3y = 58540
Simplifying the equation, we get:
1.25x + 1.3y = 58540
Now, let's consider the original total cost of RM 46000. We can set up another equation based on this information:
x + y = 46000
We now have a system of two equations:
1.25x + 1.3y = 58540
x + y = 46000
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution:
Express x in terms of y using the second equation:
x = 46000 - y
Substitute x = 46000 - y into the first equation:
1.25(46000 - y) + 1.3y = 58540
Distribute and simplify:
57500 - 1.25y + 1.3y = 58540
0.05y = 1040
Divide both sides by 0.05 to isolate y:
y = 1040 / 0.05
y = 20800
Now substitute the value of y back into the second equation to find x:
x + 20800 = 46000
x = 46000 - 20800
x = 25200
Therefore, the original cost of the construction materials (x) is RM 25200 and the cost of labor (y) is RM 20800.