Finding the Third Proportional to 785 and 1,106.50

Step by Step Solution

1. Step 1: Write the proportion equation
   785 : 1,106.50 = 1,106.50 : x
2. Step 2: Convert to fraction form
   785/1,106.50 = 1,106.50/x
3. Step 3: Cross multiply
   785x = 1,106.50 × 1,106.50
4. Step 4: Simplify right side
   785x = 1,224,342.25
5. Step 5: Solve for x
   x = 1,224,342.25/785
6. Step 6: Final answer
   x = 1,559.67