A farmer is going to build a rectangular pen. He has two plans to choose from. In Plan A, the length of the rectangle is four times the width. In Plan B, the length of the rectangle is 15 meters more than the width. For what values of the width will the perimeter in Plan A be less than that in Plan B? Use w for the width (in meters), and solve your inequality for w.

Question

anonymous · Answer

I'd like to draw this out, but the computer won't let me, so you'll have to visualize it.

pen A is a rectangle with a w on each side and a 4w on the top and bottom. Add to get perimeter. w+w+4w+4w=10w

pen B is a rectangle with a w on each side and a w+15 on the top and bottom. Add up again. w+w+ w+15+w+15=4w+30

You want a to be less than b, so set up an equation like this.     10w<4w+30

You solve inequalities like normal equations; just be ready to flip the sign if you multiply or divide the opposite side by a negative. You don't have to worry about that with this one.
10w<4w+30
6w<30
w<5

So your width can be 3, 4.999999, -200 (theoretically)... anything less than five.

anonymous · Answer

Thank you, very helpful and thorough explanation, much appreciated