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Finding the Third Proportional to 213,597 and 461,457

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Solution

The third proportional to 213,597 and 461,457 is: 996,936.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,597 : 461,457 = 461,457 : x
  2. Step 2: Convert to fraction form
    213,597/461,457 = 461,457/x
  3. Step 3: Cross multiply
    213,597x = 461,457 × 461,457
  4. Step 4: Simplify right side
    213,597x = 212,942,562,849
  5. Step 5: Solve for x
    x = 212,942,562,849/213,597
  6. Step 6: Final answer
    x = 996,936.11

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.