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Finding the Third Proportional to 213,429 and 464,442

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Solution

The third proportional to 213,429 and 464,442 is: 1,010,670.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,429 : 464,442 = 464,442 : x
  2. Step 2: Convert to fraction form
    213,429/464,442 = 464,442/x
  3. Step 3: Cross multiply
    213,429x = 464,442 × 464,442
  4. Step 4: Simplify right side
    213,429x = 215,706,371,364
  5. Step 5: Solve for x
    x = 215,706,371,364/213,429
  6. Step 6: Final answer
    x = 1,010,670.39

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.