Question

do a quantitative analysis of the following problem, and use this analysis to solve the problem meaningfully. a carpenter has a board 216 inches long and 12 inches wide. he makes 4 identical shelves and still has a piece of board 32 inches long left over. how long is each shelf? (give your answers as whole numbers.) length of board: □ inches width of board: □ inches number of shelves: □ shelves length of the board left over: □ inches length needed for all shelves: □ inches length of one shelf: □ inches

Explanation:

Step1: Identify given values

Length of board: \( 216 \) inches, Width: \( 12 \) inches, Shelves: \( 4 \), Leftover: \( 32 \) inches.

Step2: Calculate total length for shelves

Subtract leftover from total length: \( 216 - 32 = 184 \) inches (total length for 4 shelves).

Step3: Find length of one shelf

Divide total shelf length by number of shelves: \( \frac{184}{4} = 46 \) inches.

Answer:

length of board: 216 inches
width of board: 12 inches
number of shelves: 4 shelves
length of the board left over: 32 inches
length needed for all shelves: 184 inches
length of one shelf: 46 inches