Finding the Third Proportional to 802 and 1,166.50

Step by Step Solution

1. Step 1: Write the proportion equation
   802 : 1,166.50 = 1,166.50 : x
2. Step 2: Convert to fraction form
   802/1,166.50 = 1,166.50/x
3. Step 3: Cross multiply
   802x = 1,166.50 × 1,166.50
4. Step 4: Simplify right side
   802x = 1,360,722.25
5. Step 5: Solve for x
   x = 1,360,722.25/802
6. Step 6: Final answer
   x = 1,696.66