SOLUTION: A rectangular garden is surrounded by a walk or uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards, f

One way to solve this problem is to find the solution to this quadratic equation 


(16-2x)*(24-2x) = 180,   (where x = width of the walkway).



Another way is to solve the problem MENTALLY.


For it, notice that the difference in dimensions of the larger rectangle is the same as the difference in dimensions of the smaller rectangle.
and this difference is equal to 24 - 16 = 8.


So, you need to find factorization of the number 180 (the area) into the product of two factors that differ in 8 units.

Thinking 3 - 5 - 10 seconds, you will find 180 = 18*10.


So the dimensions of the garden are 18 by 10 feets.


Hence, the width of the walkway is  =  = 3 feet.