Finding the Third Proportional to 828 and 1,147.50

Step by Step Solution

1. Step 1: Write the proportion equation
   828 : 1,147.50 = 1,147.50 : x
2. Step 2: Convert to fraction form
   828/1,147.50 = 1,147.50/x
3. Step 3: Cross multiply
   828x = 1,147.50 × 1,147.50
4. Step 4: Simplify right side
   828x = 1,316,756.25
5. Step 5: Solve for x
   x = 1,316,756.25/828
6. Step 6: Final answer
   x = 1,590.29