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Finding the Third Proportional to 205,142 and 431,018

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Solution

The third proportional to 205,142 and 431,018 is: 905,599.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,142 : 431,018 = 431,018 : x
  2. Step 2: Convert to fraction form
    205,142/431,018 = 431,018/x
  3. Step 3: Cross multiply
    205,142x = 431,018 × 431,018
  4. Step 4: Simplify right side
    205,142x = 185,776,516,324
  5. Step 5: Solve for x
    x = 185,776,516,324/205,142
  6. Step 6: Final answer
    x = 905,599.62

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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.