Word Problem..

[snakeyesxlaw]

could somebody help set this word problem up;

A factory is to be built on a lot measuring 50 feet by 100 feet. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of the lawn be, and what are the dimensions of the factory?

Using x for the width of the lawn, write an expression for the area A(x) of the factory.

 

[Deleted member 4993]

could somebody help set this word problem up;

A factory is to be built on a lot measuring 50 feet by 100 feet. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of the lawn be, and what are the dimensions of the factory?

Using x for the width of the lawn, write an expression for the area A(x) of the factory.

First draw a picture

 A           100        B
  _______________________
  |    C            D    |
  | x   _____________x   |
  |    |            |    |
  |    |            |    |  50
  |    |            |    |
  |    |____________|    |
  |   E           F      |
  |______________________|

 G                      H

ABHG is the plot

CDFE is the factory

Width of the lawn is

AB = GH = 100

AG = BH = 50

CD = EF = 100 -2x

CE = DF = 50 -2x

Area of the factory = 1/2 * 50 * 100

Area of the factory = (100 -2x) * (50-2x)

Finish it now......

 

[snakeyesxlaw]

okay, this is how i finished based on the setup;

i switched the #'s around which were originally 150 x 200 feet, so the x would come out to equaling a real number.

Area of Factory = 1/2*150*200 = 1/2(30000) = 15000
Area of Factory = (200-2x)*(150-2x)

(200-2x)*(150-2x)=15000
30000 - 400x - 300x + 4x^2 = 15000
4x^2 - 700x + 3000 = 15000
4*(x^2 - 175x + 3750) = 0
4*(x-25)*(x-150) = 0

x = 25 = width of x
x = 150 = N/A = too large



thanks!

 

[Deleted member 4993]

okay, this is how i finished based on the setup;

i switched the #'s around which were originally 150 x 200 feet, so the x would come out to equaling a real number.

Area of Factory = 1/2*150*200 = 1/2(30000) = 15000
Area of Factory = (200-2x)*(150-2x)

(200-2x)*(150-2x)=15000...............................................(1)
30000 - 400x - 300x + 4x^2 = 15000
4x^2 - 700x + 3000 = 15000
4*(x^2 - 175x + 3750) = 0
4*(x-25)*(x-150) = 0

x = 25 = width of x
x = 150 = N/A = too large

You should check your answer by substituting it back into the eqn. (1).

thanks!