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Finding the Third Proportional to 102,421 and 213,017

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Solution

The third proportional to 102,421 and 213,017 is: 443,036.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,421 : 213,017 = 213,017 : x
  2. Step 2: Convert to fraction form
    102,421/213,017 = 213,017/x
  3. Step 3: Cross multiply
    102,421x = 213,017 × 213,017
  4. Step 4: Simplify right side
    102,421x = 45,376,242,289
  5. Step 5: Solve for x
    x = 45,376,242,289/102,421
  6. Step 6: Final answer
    x = 443,036.51

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.