How many blinds are needed? By how much does the total area of the blinds exceed the area of the window? A 146 cm by 90 cm window has vertical...

I have assumed the window has a vertical dimension of 90
cm and a horizontal dimension of 146 cm. Each blind has dimensions of 90 cm by 10 cm and
when it is placed it overlaps its right adjacent blind by 2
cm.

Let the total number of blinds needed be N. The blinds
at the ends have a non-overlapping area of 90*8. Each of the other binds has a
non-overlapping area of 90*6. Also, there is an area of 90*2 between any two blinds
where two blinds overlap each other.

To cover the area of
146*90 cm^2 we have 90*8*2 + (N - 2)*90*6 + (N -
1)*90*2.

=> 146 = 8*2 + (N - 2)*6 + (N -
1)*2

=> 130 = 6N - 12 + 2N -
2

=> 130 + 14 =
8N

=> 144 =
8N

=> N = 18

18 blinds
are required to cover the window.

The area of the blinds is
18*10*90 = 16200 and the area of the window is 13140. This difference between the two is
3060 cm^2.

18 blinds are needed to cover the
window. The total area of the blinds exceeds that of the window by 3060
cm^2.