Question

A new house is to have nine aluminium windows, each identical in shape to that shown in the diagram. The outer frame costs €\[8.50\] per metre and the inner slats cost €\[3.75\] per metre. Find the total cost for the framing and slats.

Answer 1

Hint:We are given that a house is to have nine aluminium windows. We are given the cost of the outer frame per meter and the cost of the inner slats per meter. We are asked to find the total cost of the framing and the slats. To find the cost of framing one window, we will first find the perimeter of the window and then multiply it to the per meter cost. Then, to find the cost of inner slats, we will first calculate the lengths of the slats and then multiply it with the per meter cost. Now, we will add up the cost of framing and slats to get the cost of one window. Since we have nine such windows, we will multiply by 9 to get the total cost of framing and slats of the nine windows.

Complete step-by-step solution:
According to the given question, we are given a house to have nine aluminium windows. We are given the cost of the outer frame per meter and the cost of the inner slats per meter. We are asked to find the total cost of the framing and the slats.
We will first find the cost of one window and multiply with 9 to find the cost of the nine windows.
We have,
The cost of outer frame per meter = €\[8.50\]
We will find the perimeter of the window first. The window is in the shape of a rectangle, so we have,
Length of the window = \[2m\]
Breadth of the window = \[1.5m\]
Perimeter of the window = \[2\left( l+b \right)\]
\[\Rightarrow 2\left( 2+1.5 \right)\]
\[\Rightarrow 2\left( 3.5 \right)\]
\[\Rightarrow 7m\]
Cost of outer framing = €\[8.50\times 7\]
\[\Rightarrow \]€\[59.5\]

Now, to find the length of the inner slats we will add up the horizontal and the vertical lengths of the slats, we have,
Total length of the slats = \[2\left( 3 \right)+1.5\left( 3 \right)\]
\[\Rightarrow 6+4.5\]
\[\Rightarrow 10.5m\]
Cost of inner slats per meter = €\[3.75\]
So, cost of inner slats = €\[3.75\times 10.5\]
\[\Rightarrow \]€\[39.37\]

The total cost of framing one window (including outer frames and the inner slats) = \[59.5+39.37\]
\[\Rightarrow \]€\[98.87\]
If one window costs €\[98.87\]
Nine windows will cost = €\[98.87\times 9\]
\[\Rightarrow \]€\[889.83\]
Therefore, the total cost of framing and slats is €\[889.83\].

Note: The cost of framing and slats should be calculated separately and should not be calculated together as it might lead to expressions getting complicated. Also, we have to find the total cost of framing and the slats of nine windows. So, after finding the cost for one window, do not forget to multiply with 9 to get the total cost of all the nine windows.