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Finding the Third Proportional to 261,914 and 409,719

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Solution

The third proportional to 261,914 and 409,719 is: 640,934.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    261,914 : 409,719 = 409,719 : x
  2. Step 2: Convert to fraction form
    261,914/409,719 = 409,719/x
  3. Step 3: Cross multiply
    261,914x = 409,719 × 409,719
  4. Step 4: Simplify right side
    261,914x = 167,869,658,961
  5. Step 5: Solve for x
    x = 167,869,658,961/261,914
  6. Step 6: Final answer
    x = 640,934.27

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.