Understanding the Wood Cutting Problem

The video tutorial explains how to solve a problem involving cutting a 32-inch piece of wood into two parts, where one part is 8 inches longer than the other. The process involves modeling the problem using variables, setting up an equation, and solving it to find the length of the shorter piece. The solution is verified by checking the sum of the lengths.

What is the total length of the wood before it is cut?

• 24 inches

• 32 inches

• 40 inches

• 16 inches

How much longer is the longer piece compared to the shorter piece?

• 5 inches

• 10 inches

• 8 inches

• 12 inches

What variable is used to represent the length of the shorter piece?

• Y

• Z

• W

• X

How is the length of the longer piece expressed in terms of the shorter piece?

• X + 12

• X + 10

• X + 8

• X + 5

What equation represents the total length of the wood pieces?

• X + X + 8 = 36

• X + X + 8 = 40

• X + X + 8 = 32

• X + X + 8 = 24

What is the first step in solving the equation for X?

• Subtract 8 from both sides

• Add 8 to both sides

• Multiply both sides by 2

• Divide both sides by 2

After combining like terms, what does the equation become?

• 2X + 8 = 40

• 2X + 8 = 24

• 2X + 8 = 32

• 2X + 8 = 36

What is the length of the shorter piece of wood?

• 16 inches

• 10 inches

• 14 inches

• 12 inches

How do we verify that the solution is correct?

• Check if the sum is 40

• Check if the sum is 36

• Check if the sum is 32

• Check if the sum is 24