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Finding the Third Proportional to 213,698 and 457,042

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Solution

The third proportional to 213,698 and 457,042 is: 977,488.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,698 : 457,042 = 457,042 : x
  2. Step 2: Convert to fraction form
    213,698/457,042 = 457,042/x
  3. Step 3: Cross multiply
    213,698x = 457,042 × 457,042
  4. Step 4: Simplify right side
    213,698x = 208,887,389,764
  5. Step 5: Solve for x
    x = 208,887,389,764/213,698
  6. Step 6: Final answer
    x = 977,488.74

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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.