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Finding the Third Proportional to 413,834 and 661,199

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Solution

The third proportional to 413,834 and 661,199 is: 1,056,423.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,834 : 661,199 = 661,199 : x
  2. Step 2: Convert to fraction form
    413,834/661,199 = 661,199/x
  3. Step 3: Cross multiply
    413,834x = 661,199 × 661,199
  4. Step 4: Simplify right side
    413,834x = 437,184,117,601
  5. Step 5: Solve for x
    x = 437,184,117,601/413,834
  6. Step 6: Final answer
    x = 1,056,423.87

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.