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Finding the Third Proportional to 213,414 and 457,257

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Solution

The third proportional to 213,414 and 457,257 is: 979,710.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,414 : 457,257 = 457,257 : x
  2. Step 2: Convert to fraction form
    213,414/457,257 = 457,257/x
  3. Step 3: Cross multiply
    213,414x = 457,257 × 457,257
  4. Step 4: Simplify right side
    213,414x = 209,083,964,049
  5. Step 5: Solve for x
    x = 209,083,964,049/213,414
  6. Step 6: Final answer
    x = 979,710.63

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.