SOLUTION: Hello I have been trying to figure out this word problem and not sure why I keep getting the answers wrong, I would really appreciate any help.
"A rectangular flower garden has a
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Question 976537: Hello I have been trying to figure out this word problem and not sure why I keep getting the answers wrong, I would really appreciate any help.
"A rectangular flower garden has a length that is 3 feet less then twice its width. A 3-foot brick border is added around the garden, and the area of the garden and the brick border is a total of 143 square feet. Find the dimensions of the garden without the brick border. The length is _____ feet and the width is ____ feet."
Found 2 solutions by solver91311, josgarithmetic:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If you keep getting the answers wrong, then you must have tried to do this problem more than once. Please share what you did and the answer you obtained on one of these attempts.
John
My calculator said it, I believe it, that settles it
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
This kind of exercise is very common and a generalized solution is useful.
The rectangular garden is dimensions x and y. The uniform border around the garden is the uniform width u.
Also let A be the area (at ground level only) of the border.
Summary of Variables:
x=unknown
y=-3+2x
u=3
A=143
-
Find x and y.
Garden Area, ;
Total Area, ;
Just the brick border ground-level area, .
-
The last equation is in the single unknown variable, x. The other variables are given, known.
Simplify the border area equation.
---skipping several steps, reach .
------formula for the unknown variable, all in symbols.
Evaluate x according to the given values for A, and u.
Evaluate y using the now found x value.
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