SOLUTION: Would someone be so kind as to assist me with this problem? A football field is about 50 yards wide by 120 yards long. The border of uniform width around the entire field has an ar

Algebra.Com
Question 249526: Would someone be so kind as to assist me with this problem? A football field is about 50 yards wide by 120 yards long. The border of uniform width around the entire field has an area of about 1800 square yards. How wide is the border around the field?
This is how I have attempted to solve the problem:
(120-2x)(50-2x)=6000-1800 length x width minus the two sides of each rep by x
6000-240x-100x+4x^2=4200
4x^2-240x-100x+6000-4200=
4x^2-340x+1800=0
4(x-5)(x-90)
this is where x should equal the width of the border, but 5 does not work, what am I doing wrong?
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Assuming that the problem has the correct numbers (ie there are no typos in the book), you're doing great until you reach the point where you try to factor. It turns out that can't be factored at all (over the rationals). So we must use the quadratic formula to solve



Start with the given equation.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "x":


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Subtract from to get


Multiply and to get .


Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


or Break up the expression.


So the solutions are or


which approximate to or


However, take note that when . So may be a solution, but it doesn't make sense in this problem since you can't have a negative width.


So the only value that makes sense is


This means that the width of the border is about 5.673 yards. Normally, you'd get a clean number. It's not guaranteed, but books tend to fix problems so nice solutions result. So I'd double check the problem.
RELATED QUESTIONS

can you help me with this last problem; solve using the 5 step problem process a... (answered by richwmiller,Nate)
a football field is about 50 yards wide by 120 yards long. the border of uniform width... (answered by scott8148)
Show all steps necessary to arrive at your solution. A football field is about 50... (answered by oberobic)
A football field is 40 yards wide and 120 yards long. Find the distance between opposite... (answered by richwmiller)
The school's custodian is mowing the grass on the football field by cutting a border... (answered by ankor@dixie-net.com)
A football field is 120 yards long and 53 yards wide. How much fencing is needed to... (answered by checkley79)
A football field is 40 yards wide and 120 yards long. Find the distance between opposite... (answered by richwmiller)
A rectangular soccer field is 120 yards (360 feet) long by 64 yards (192 feet) wide. What (answered by CubeyThePenguin)
A regulation football field is 100 yards long and 53 1/3 yards wide. How many square... (answered by Alan3354)