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Finding the Third Proportional to 205,145 and 431,024

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Solution

The third proportional to 205,145 and 431,024 is: 905,611.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,145 : 431,024 = 431,024 : x
  2. Step 2: Convert to fraction form
    205,145/431,024 = 431,024/x
  3. Step 3: Cross multiply
    205,145x = 431,024 × 431,024
  4. Step 4: Simplify right side
    205,145x = 185,781,688,576
  5. Step 5: Solve for x
    x = 185,781,688,576/205,145
  6. Step 6: Final answer
    x = 905,611.58

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.