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Finding the Third Proportional to 257,536 and 409,792

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Solution

The third proportional to 257,536 and 409,792 is: 652,062.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,536 : 409,792 = 409,792 : x
  2. Step 2: Convert to fraction form
    257,536/409,792 = 409,792/x
  3. Step 3: Cross multiply
    257,536x = 409,792 × 409,792
  4. Step 4: Simplify right side
    257,536x = 167,929,483,264
  5. Step 5: Solve for x
    x = 167,929,483,264/257,536
  6. Step 6: Final answer
    x = 652,062.17

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.