Finding the Third Proportional to 164.50 and 177.50

Step by Step Solution

1. Step 1: Write the proportion equation
   164.50 : 177.50 = 177.50 : x
2. Step 2: Convert to fraction form
   164.50/177.50 = 177.50/x
3. Step 3: Cross multiply
   164.50x = 177.50 × 177.50
4. Step 4: Simplify right side
   164.50x = 31,506.25
5. Step 5: Solve for x
   x = 31,506.25/164.50
6. Step 6: Final answer
   x = 191.53