SOLUTION: I just can't figure out how to solve this word problem. I get confused with fractions. An architect designs a rectangular flower garden such that the width is two-thirds of th

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Question 265319: I just can't figure out how to solve this word problem. I get confused with fractions.
An architect designs a rectangular flower garden such that the width is two-thirds of the length. If 260 feet of antigue picket fencing are to be used to enclose the garden, find the dimensions of the garden.
I am so confused and would really appreciate help with this one!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An architect designs a rectangular flower garden such that the width is two-thirds of the length.
If 260 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.
:
This is a perimeter problem
2L + 2W = 260
:
It says,"the width is two-thirds of the length.", therefore we can write:
W = 2%2F3L
:
Substitute 2%2F3L for W in the perimeter equation
2L + 2(2%2F3L) = 260
which is
2L + 4%2F3L = 260
Get rid of the denominator multiply both sides by 3, results
3(2L) + 4L = 3(260)
6L + 4L = 780
10L = 780
L = 780%2F10%29
L = 78 ft is the length
and
2%2F3(78) = 52 ft is the width
:
:
Check solutions by finding the perimeter
2(78) + 2(52) =
156 + 104 = 260; confirms our solution