Question

select the correct answer.
a wooden plank of length x is cut into 8 sections such that each section is at most $2\frac{1}{2}$ meters long. what is the length of the entire plank in meters?
\\(\bigcirc\\) a. \\(x \leq 3.2\\) meters
\\(\bigcirc\\) b. \\(x \leq 20\\) meters
\\(\bigcirc\\) c. \\(x \geq 10.5\\) meters
\\(\bigcirc\\) d. \\(x \geq 20\\) meters

Explanation:

Step1: Understand the problem

The plank of length \( x \) is cut into 8 sections, and each section is at most \( 2\frac{1}{2} \) meters long. So the total length \( x \) should be at most the sum of 8 sections each of length \( 2\frac{1}{2} \) meters. First, convert \( 2\frac{1}{2} \) to an improper fraction or decimal. \( 2\frac{1}{2}=\frac{5}{2} = 2.5 \) meters.

Step2: Calculate the total maximum length

To find the total maximum length, multiply the number of sections (8) by the length of each section (\( 2.5 \) meters). So \( x\leq8\times2.5 \).

Step3: Compute the product

Calculate \( 8\times2.5 \). \( 8\times2.5 = 20 \). So \( x\leq20 \) meters.

Answer:

B. \( x \leq 20 \) meters