Final answer:
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.