Finding the Third Proportional to 536 and 1,172.50

Step by Step Solution

1. Step 1: Write the proportion equation
   536 : 1,172.50 = 1,172.50 : x
2. Step 2: Convert to fraction form
   536/1,172.50 = 1,172.50/x
3. Step 3: Cross multiply
   536x = 1,172.50 × 1,172.50
4. Step 4: Simplify right side
   536x = 1,374,756.25
5. Step 5: Solve for x
   x = 1,374,756.25/536
6. Step 6: Final answer
   x = 2,564.84