Question

Given that point A is between points X and Z, and XA = 22 inches, AZ = (16x) inches, and XZ = (22x – 32) inches, can you determine the length of AZ in inches? Please provide the value for AZ.

Answer 1

To find the length of AZ in inches, we set up an equation relating XA, AZ, and XZ. Solving for x gives us x = 9, and consequently, the length of AZ is 144 inches.

Step-by-step explanation:

To solve for the length of AZ in inches, we need to set up an equation using the information provided. Since point A is between points X and Z, the sum of XA and AZ must equal the total distance XZ. Using the given lengths, we have:

XA + AZ = XZ

22 inches + (16x) inches = (22x - 32) inches

Now, we can solve for x. After finding x, we can find the length of AZ in inches by multiplying 16 times the value of x.

Solving for x:

22 + 16x = 22x - 32

Moving all the terms with x on one side and the constants on the other:

32 + 22 = 22x - 16x

54 = 6x

x = 9

Now that we know x, we can calculate the length of AZ:

AZ = 16 × x

AZ = 16 × 9

AZ = 144 inches

Therefore, the length of AZ is 144 inches.