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A new department store needs a new rectangular parking lot to encompass the store. The front of the department store is 200 feet wide and the store is 100 feet deep. The front of the store faces north. The contractor wants the width of the parking lot on the south and east sides of the store to be the same. Also, the width of the parking lot on the north side is to be 8 times as wide as the south and the width of the parking lot on the west side is to be 10 times as wide as the east. When completed, the parking lot will be 38,900 square feet of blacktop. How wide is the west parking lot?

Verified Answer :

nevaeh1448247

The store's dimensions are 200 ft on the north and south side and 100 feet on the east and west sides. 

To this add the following amount of blacktop. 

E = x 
S = x 
W = 10x 
N = 8x 

So the store's lot is going to be 200 + E + W = 200 + 11x from east to west and 100 + N + S = 100 + 9x from north to south. 

The total area of the space occupied is (200 + 11x)(100 + 9x) = 20000 + 2900x + 99x^2 

From this, subtract the area of the store (200 x 100 = 20000) 

And what you get is that 99x^2 + 2900x = 38900 for the amount of blacktop needed to pave this parking lot. 

99x^2 + 2900x - 38900 = 0 

x = (-2900 +/- sqrt(2900^2 - 4 99 -38900)) / (2 * 99) 
x = (-2900 +/- sqrt(8410000 + 15404400)) / 198 
x = (-2900 +/- sqrt(23814400)) / 198 
x = (-2900 +/- 4880) / 198 
x = --7780/198 or 1980/198 
x = 10 

The west side of the parking lot is 100 feet.

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