solve the problem.
the length of a rectangular flower bed is 7 feet less than 3 times its width. the area of the bed is 20 feet squared. find the dimensions of the flower bed.
Let x = width, and thus the length = 3x-7
Area = x(3x-7) = 20
Solve for x ,
x = 4 ft
3x-7 = 5 ft
Answer: 4 ft x 5 ft
Let W be the width in feet. Translating the first sentence we see that the length is L = 3W - 7.
The area is given by A=LW so we get:
(3W - 7)W = 20
3W2 - 7W - 20 = 0
(3W + 5)(W - 4) = 0
W = -5/3 or W = 4.
However, the width can't be negative. Thus W = 4 and L = A/W = 20/4 = 5.
we can double-check that this works: 3*4 - 7 = 12 - 7 = 5.
So it is a 5 ft. x 4 ft. (L x W) flower bed.