The schools custodian is mowing the grass on the football fi

The school\'s custodian is mowing the grass on the football field by cutting a border around the field. The field is 120 yards long and 50 yards wide. How wide will the border be when he has mowed half of the area of the football field?

Solution

Find half the area of the field:
.5 * 120 * 50 = 3000 sq/yds
:
Let x = the width of the cut border
:
(120-2x)*(50-2x) = 3000
FOIL
6000 - 240x - 100x + 4x^2 = 3000
:
4x^2 - 340x + 6000 - 3000 = 0
:
4x^2 - 340x + 3000 = 0
simplify, divide by 4
x^2 - 85x + 750 = 0
factor
(x-75)(x-10) = 0
:
x = 10 yds is the reasonable solution
:
:
check by finding the area of the un-mowed part
(120-20) * (50-20) = 3000