SOLUTION: Wendy, a landscaper, who just completed 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 b

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Question 348189: Wendy, a landscaper, who just completed 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F.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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation; a=4; b=80; c=-324
x+=+%28-80+%2B-+sqrt%2880%5E2-4%2A4%2A-324+%29%29%2F%282%2A4%29+
:
x+=+%28-80+%2B-+sqrt%286400+-%28-5184%29+%29%29%2F8+
:
x+=+%28-80+%2B-+sqrt%286400+%2B+5184+%29%29%2F8+
:
x+=+%28-80+%2B-+sqrt%2811584%29%29%2F8+
The positive solution only wanted here
x+=+%28-80+%2B+107.629%29%2F8+
x = 27.629%2F8
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%2F27 = 3 cu/yds