SOLUTION: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of u

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Question 95706This question is from textbook
: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, 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?
Thanks so much for your help! I'm pulling my hair out.
Connie This question is from textbook

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
START BY DRAWING A SKETCH OF THE 6 BY 10 PLOT. NOW DRAW A SMALL BORDER AROUND IT & LABEL THE WIDTH X.
THE AREA TO BE FILLED IN IS:
(6+2X)+(10+2X)-6*10
60+20X+12X+4X^2-60
4X^2+32X IS THE AREA TO BE CEMENTED TO A DEPTH OF 3 INCHES WHICH IS 3/12 FEET OR .25 FEET.
THE AMOUNT OF CEMENT IN FEET IS 38383=27 CUBIC FEET.
NEW WE SOLVE FOR THE VALUE OF X:
(4X^2+32X)*.25=27
X^2+8X-27=0
USING THE QUADRATIC EQUATION WE GET:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(-8+-SQRT[8^8-4*1*-27])/281
X=(-8=-SQRT(64*108])/2
X=(-8+-SQRT172)/2
X=(-8+-13.11)/2
X=(-8+13.11)/2
X=5.11/2
X=2.56 FEET IS THE WIDTH OF THE BORDER NEEDED FOR THE 27 CUBIC FEET OF CEMENT.
FILL IN THESE MEASUREMENTS IN YOUR DIAGRAM AND VERIFY THE ANSWERS OR 2.56 FEET FOR THE WIDTH & .25 FEET FOR THE DEPTH.