SOLUTION: Please help me to solve it! A gardener would like to plant a patch of peas. In order to harvest enough peas patch should have 300 quare feet of peas. In order to have convenient

Algebra ->  Linear-equations -> SOLUTION: Please help me to solve it! A gardener would like to plant a patch of peas. In order to harvest enough peas patch should have 300 quare feet of peas. In order to have convenient      Log On


   

Question 211763: Please help me to solve it!
A gardener would like to plant a patch of peas. In order to harvest enough peas patch should have 300 quare feet of peas. In order to have convenient access, there will be a walkway 18 inches wide running down the middle of the patch, both width-wise and length-wide. For ascetic purposes the patch should have a length to width ratio of 8:5. What are the outer dimensions of the pea patch? If the gardener only walks around the edge or on the walkways in the middle, then what will be the farthest the gardener has to reach to weed the peas?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In order to harvest enough peas patch should have 300 square feet of peas.
In order to have convenient access, there will be a walkway 18 inches wide
running down the middle of the patch, both width-wise and length-wide.
For ascetic purposes the patch should have a length to width ratio of 8:5.
What are the outer dimensions of the pea patch?
:
I picture this as two 1.5' wide walkways running both ways thru the middle of the rectangle,
and the area of the walkway not included in the 300 sq/ft
:
Let x = the multiplier of the length and width
then
8x = length
5x = width
:
The two walkways will subtract 1.5 ft from both dimensions so we have:
(8x - 1.5)*(5x - 1.5) = 300
FOIL
40x^2 - 12x - 7.5x + 2.25 = 300
:
40x^2 - 19.5x + 2.25 - 300 = 0
:
40x^2 - 19.5x - 297.75 = 0
:
Use the quadratic formula; a=40; b=-19.5; c=-297.75
:
The positive solution: x=2.98 is the multiplier
:
2.98*8 = 23.84 ft is the length
2.98*5 = 14.9 ft is the width
:
If the gardener only walks around the edge or on the walkways in the middle,
then what will be the farthest the gardener has to reach to weed the peas?
:
From the path down the middle lengthwise and from the outside;
That would be 14.9%2F4 = 3.725 ft
:
Confirm that we have 300 sq/ft for bean planting
(23.84 - 1.5) * (14.9 - 1.5) =
22.34 * 13.4 = 299.356 ~ 300