Question 346695
 a rectangular flower garden measuring 25 feet by 15 feet,
 orders 3 cubic yards of pre-mixed cement, all of which is to be used to
 create a border of uniform width around the garden.
 If the border is to have a depth of 3 inches, how wide will the border be?
:
Find the area of the garden
25 * 15 = 375 sq/ft
:
Find the area of the border by dividing 3 cu/yds by 3 inches 
Change 3 cu/yds to cu/ft:  3 * 27 = 81 cu/ft
Change 3 inches to .25 ft
{{{81/.25}}} = 324 sq/ft is the area of the border
:
The total area of the garden and the border
375 + 324 = 699 sq/ft
:
Let x = the width of the border
:
The equation for the total area
(2x+25)*(2x+15) = 699
FOIL
4x^2 + 30x + 50x + 375 = 699
4x^2 + 80x + 375 - 699 = 0
4x^2 + 80x - 324 = 0
Use the quadratic formula to find x
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this equation; a=4; b=80; c=-324
{{{x = (-80 +- sqrt(80^2-4*4*-324 ))/(2*4) }}}
:
{{{x = (-80 +- sqrt(6400 -(-5184) ))/8 }}}
:
{{{x = (-80 +- sqrt(6400 + 5184 ))/8 }}}   
:
{{{x = (-80 +- sqrt(11584))/8 }}}
The positive solution only wanted here
{{{x = (-80 + 107.629)/8 }}}
x = {{{27.629/8}}}
x = 3.45 ft is the width of the border  
:
:
:
Check solution, 2x = 6.9
(6.9+25)*(6.9+15) = 699 sq/ft, total area
Subtract the area of the garden: 699 - 375 = 324, the area of the border
Find the volume of the border (mult by 3" which is .25 ft: 324*.25 = 81 cu/ft
Find 81 cu/ft in cu/yds: {{{81/27}}} = 3 cu/yds