Board Feet Measurement

Some lumber can be purchased based on standard sizes, such as 2x4-8 which means a board 8 feet long by 4 inches wide by 2 inches thick on the cross-section.  Hardwood lumber, usually used in cabinets or furniture, is purchased based on board feet.  A board foot is any piece of wood that is 144 cubic inches in volume, usually described as a piece of wood 12 inches long by 12 inches wide by 1 inch thick.  The formula for computing the price P of a board with dimensions x inches long by y inches wide by z inches thick with unit price p (per board foot) is

Given a  1x4-6 board, that is 6 feet long by 8 inches wide by 1 inch thick, find the price of the board if the price is $2.50 per board foot.

Answer:  Replacing x with 72 inches (6 feet x 12 in/feet), y with 8 inches, z with 1 inch, and p with 2.50 yields a total price of $10.00.

1. Find the cost of a 2x10-8 board with a unit cost of $2.
2. How long can a 1x6 board be if you have $20 to pay for the board and the unit price is $2.50?
3. What is the unit price p of a 4x4-6 board that costs $22?
4. If the length of the boards are always given in feet measurements, how could you adjust the formula so that x would represent length in feet?
5. Search online for wood furniture plans.  Select one, and use their material list (or create your own from their drawings) to compute the cost of the wood necessary to build the furniture.  You will need to find the unit cost for the type of wood you would use.