MATH HELP NEEDED...area of rectangle

Question

The ratio of the width to the length of a given rectangle is 2 to 3. If the width and length are increased by 4 inches, the area of the resulting rectangle is 80 square inches. Find the width and length of the original rectangle.

Answer 1

Let x = the width

Let y = the length

x/y = 2/3

3x = 2y

y = (3/2)x

(x + 4)(y + 4) = 80

(x + 4)(3/2 x + 4) = 80

(3/2)x² + 10x + 16 = 80

(3/2)x² + 10x - 64 = 0

3x² + 20x -128 = 0

(3x + 32)(x - 4) = 0

3x + 32 = 0

3x = -32

x = -32/3, illogical answer

x - 4 = 0

x = 4 inches

y = (3/2)(4)

y = 6 inches