Question 1126574: A landscaper, who just completed a rectangular flower garden measuring 6 ft by 10 ft, orders 1 cubic yard of premixed 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? (1 cubic yard = 27 cubic feet)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! landscaper, who just completed a rectangular flower garden measuring 6 ft by 10 ft, orders 1 cubic yard of premixed 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?
(1 cubic yard = 27 cubic feet)
:
3" = .25 ft
find the area of the concrete border, 27/.25 = 108 sq/ft
find the area of the garden, 6*10 = 60 sq/ft
Total area of the garden and the border; 108 + 60 = 168 sq/ft
:
let x = the width of the concrete border
then the overall length and width (garden & border):
(2x+10) by (2x+6)
:
(2x+10)*(2x+6) = 168
FOIL
4x^2 + 12x + 20x + 60 = 168
4x^2 + 32x + 60 - 168 = 0
A quadratic equation
4x^2 + 32x - 108 = 0
simplify divide by 4
x^2 + 8x - 27 = 0
use the quadratic formula; a=1; b=8; c=-27
the positive solution
x = 2.5574 ft which is about: 2 ft 6.7 inches
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