Finding the Third Proportional to 507 and 1,256.25

Step by Step Solution

1. Step 1: Write the proportion equation
   507 : 1,256.25 = 1,256.25 : x
2. Step 2: Convert to fraction form
   507/1,256.25 = 1,256.25/x
3. Step 3: Cross multiply
   507x = 1,256.25 × 1,256.25
4. Step 4: Simplify right side
   507x = 1,578,164.06
5. Step 5: Solve for x
   x = 1,578,164.06/507
6. Step 6: Final answer
   x = 3,112.75