SOLUTION: Gwen is planting red tulips in a rectangular flowerbed that is 2 feet longer than it is wide. She plans to surround the tulips with a border of daffodils that is 2 feet wide. If th

Question 190541: Gwen is planting red tulips in a rectangular flowerbed that is 2 feet longer than it is wide. She plans to surround the tulips with a border of daffodils that is 2 feet wide. If the total area is 224 square feet, and she plants 36 daffodils per square foot, then how many daffodils does she need?
Answer by jonvaliente(64) (Show Source): You can put this solution on YOUR website!
Let x=width
. x+2=length ("2 feet longer that it is wide")
.
Area with 2-feet border = 224
The 2-feet border will add 4 feet to both width and legth of the flowerbed.
.
x+4 = width of the flowerbed with border
x+2+4 or x+6= length of the flowerbed with border
.
Area=length x width, so:
.
(x+4)*(x+6)=224
.
Solving for x, we get:
.

.
Subtracting 224 from both sides we get:
.

.
Factoring, we get:
.

.
x+20=0 and/or x-10=0
.
if x+20=0, then:
.
x+20-20=0-20 or x=-20
Since the width cannot be negative then this cannot be a solution,
.
If x-10=0, then:
.
x-10+10=0+10 or x=10
Therefore the width of the flowerbed is 10feet and the length is x+2 or 10+2 or 12 feet
.
The area of the flower bed without the border is 10x12=120 square feet
.
So the area of the border should be 224-120=104 square feet
.
36 daffodils per square foot of border, then 104*36=3744 daffodils
.
The answer is 3744 daffodils

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