Finding the Third Proportional to 416 and 521.50

Step by Step Solution

1. Step 1: Write the proportion equation
   416 : 521.50 = 521.50 : x
2. Step 2: Convert to fraction form
   416/521.50 = 521.50/x
3. Step 3: Cross multiply
   416x = 521.50 × 521.50
4. Step 4: Simplify right side
   416x = 271,962.25
5. Step 5: Solve for x
   x = 271,962.25/416
6. Step 6: Final answer
   x = 653.76