Question

DIC DEEPER A woodworker has 3 planks of wood. Each plank has a different thickness. When stacked, the thickness of the 3 planks is (6)/(8) inch. What is the possible thickness of each plank? (6)/(8) i

Answer 1

The possible thickness of each plank is (1)/(20), (3)/(40), and (1)/(10) inches.

Step-by-step explanation:

By constructing a system of equations, we can determine the potential thickness of every plank. Assume that the first plank is x inches thick, the second is y inches thick, and the third is z inches thick. The thickness of all three planks added together equals (6)/(8) inches, or x + y + z = (6)/(8). The exact values of x, y, and z cannot be determined because each plank has a different thickness. On the other hand, we can articulate them using a standard ratio. Let's take an example where an is a constant and we have x = 2a, y = 3a, and z = 4a. The result of entering these values into the formula is 2a + 3a + 4a = (6)/(8). Solving this equation, we find a = (1)/(40). Therefore, the possible thickness of each plank would be 2a = (1)/(20), 3a = (3)/(40), and 4a = (1)/(10) inches.