[Mathematics: Pre-Calculus] Word Problem

Doing some math over the summer to help me prepare for college next year, and in this one book, even though I looked up the answer, I have no idea how to get it to work. So, show your work, kthnx.

Here is the problem:

A portion of a wire 70 inches in length is bent to form a rectangle having the greatest possible area such that the length of the rectangle exceeds three times its width by 2 inches, and the dimensions of the rectangle are whole numbers. Find the length of the wire that is not used to form the rectangle.

The answer is two inches. I need the work more than anything, though. An explanation of how you get that answer would be LOVELY. ^^; Thank you.

What does it mean that it exceeds 3 times it's width by 2 inches? If I think I get what you're meaning, is this it: 3x+2 for the length and plain x for the width?

The perimeter of the rectangle is 2x+2y. As y=3x+2, this perimeter can also be expressed as 2x+2(3x+2)=8x+4<70, meaning 8x<66. As the dimensions are whole numbers, x can be 8 at most, meaning y can be 26 at most. Using these figures in the perimeter yields 2(8)+2(26)=68, leaving 2 inches.

Originally Posted by Project 2501

The perimeter of the rectangle is 2x+2y. As y=3x+2, this perimeter can also be expressed as 2x+2(3x+2)=8x+4<70, meaning 8x<66. As the dimensions are whole numbers, x can be 8 at most, meaning y can be 26 at most. Using these figures in the perimeter yields 2(8)+2(26)=68, leaving 2 inches.

Thank you muchly. ^-^