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 blinds of width 10 cm. Each blind overlaps its right...

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 blinds of width 10 cm. Each blind overlaps its right adjacent blind by 2 cm.

justaguide | College Teacher | (Level 2) Distinguished Educator

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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.