John is designing a redwood deck. Each board is 5 1/2 inches wide, and each will be placed parallel to one another. Should he use 3/16 inch, 1/4 inch, or 3/8 inch spacing between boards if he wants the deck to be as close as possible to, but not greater than, 18 feet wide? How wide will his deck be?

You would want to add the gap to the board width and then divide that number into 18 feet (216 inches). Divide to the whole number and calculate the remainder, the smallest remainder would be the closest to 18 feet.

Here, let me help you set up one of the equations.

Divide the following with a remainder:

\frac{216}{5 \frac{1}{2} + \frac{3}{16}}

Try it from here and let us know if you need more help.