Finding the Third Proportional to 838 and 1,297.50

Step by Step Solution

1. Step 1: Write the proportion equation
   838 : 1,297.50 = 1,297.50 : x
2. Step 2: Convert to fraction form
   838/1,297.50 = 1,297.50/x
3. Step 3: Cross multiply
   838x = 1,297.50 × 1,297.50
4. Step 4: Simplify right side
   838x = 1,683,506.25
5. Step 5: Solve for x
   x = 1,683,506.25/838
6. Step 6: Final answer
   x = 2,008.96