Question

A puppy pen is 1 foot longer than twice its width. John wants to increase the length and width by 5 feet each to enlarge the area by 90 square feet. What will be the area of the new pen?

Answer 1

Assume width = W
Length = 2W + 1 (because “the length is 1 foot longer than twice its width”)
Area = Length x Width = W(2W + 1)

New Width = old Width + 5 = (W + 5) (because John increases the Width by 5 feet)
New Length = old Length + 5 = (2W + 1) + 5 = (2W + 6) (because John increases the Length by 5 feet)

New Area = New Length x New Width = (2W + 6)(W + 5)

Increase in Area = New Area – old Area = (2W + 6)(W + 5) - W(2W + 1) = 90 (because the area increased by 90)

Expand the expression and solve for W:
(2W + 6)(W + 5) - W(2W + 1) = 90

Once you solve for W, plug the value into the equation for New Area, which is, (2W + 6)(W + 5) and you will get the answer to the question.