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Finding the Third Proportional to 257,696 and 409,968

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Solution

The third proportional to 257,696 and 409,968 is: 652,217.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,696 : 409,968 = 409,968 : x
  2. Step 2: Convert to fraction form
    257,696/409,968 = 409,968/x
  3. Step 3: Cross multiply
    257,696x = 409,968 × 409,968
  4. Step 4: Simplify right side
    257,696x = 168,073,761,024
  5. Step 5: Solve for x
    x = 168,073,761,024/257,696
  6. Step 6: Final answer
    x = 652,217.19

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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.