SOLUTION: A landscape artist has included a rectangular flower bed measuring 9 feet by 5 feet in her plans for a new building. She wants to use two colors of flowers in the bed, one in the c

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Question 934932: A landscape artist has included a rectangular flower bed measuring 9 feet by 5 feet in her plans for a new building. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plans to cover 24 square feet for the border, how wide can the border be?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The smaller perimeter of the border is on the inside of the whole flower bed, and not surrounding it. The area total of 9 feet by 5 feet includes the border and the "center".

Let u be the uniform width of the border on the inside of the flower bed area.

Whole flower bed area, 9*5.
Center inner flower bed, %289-2u%29%285-2u%29.
Border around the center inner bed, the area, highlight_green%289%2A5-%289-2u%29%285-2u%29=24%29.

Do the arithmetic and number property steps.
9%2A5-%289%2A5-18u-10u%2B4u%5E2%29=24
18u%2B10u-4u%5E2=24
-28u%2B4u%5E2=-24
-7u%2Bu%5E2=-6
u%5E2-7u%2B6=0
highlight%28%28u-6%29%28u-1%29=0%29.
One of the solutions will make sense but the other will not.

The uniform width size is 1 foot.