Question

Jackson is building a deck and has the choice of 2 sizes of lumber. The first two numbers represent the shape of the board and the last number is length of the board. Compute the unit rate for each product and identify the better deal (cheapest unit price). 2ft x 4ft x 16ft costs $11.76 for each board, and 2 ft x 4ft x 14ft cost $10.12 for each board.

Options:
A) The unit rate for 2ft x 4ft x 16ft is $0.245/ft^3, and for 2ft x 4ft x 14ft is $0.287/ft^3.
B) The unit rate for 2ft x 4ft x 16ft is $0.147/ft^3, and for 2ft x 4ft x 14ft is $0.164/ft^3.
C) The unit rate for 2ft x 4ft x 16ft is $0.183/ft^3, and for 2ft x 4ft x 14ft is $0.215/ft^3.
D) The unit rate for 2ft x 4ft x 16ft is $0.258/ft^3, and for 2ft x 4ft x 14ft is $0.296/ft^3.

Answer 1

To calculate the unit rate, divide the cost of each board by the volume of the board. The better deal is the 2ft x 4ft x 14ft board with a unit rate of $0.090/ft^3.

Step-by-step explanation:

To calculate the unit rate, we divide the cost of each board by the volume of the board.

For the 2ft x 4ft x 16ft board, the volume is 2 * 4 * 16 = 128 ft^3. Therefore, the unit rate is $11.76 / 128 ft^3 = $0.092/ft^3.

For the 2ft x 4ft x 14ft board, the volume is 2 * 4 * 14 = 112 ft^3. Therefore, the unit rate is $10.12 / 112 ft^3 = $0.090/ft^3.

Comparing the unit rates, the better deal is the 2ft x 4ft x 14ft board with a unit rate of $0.090/ft^3.