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Finding the Third Proportional to 413,214 and 638,047

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Solution

The third proportional to 413,214 and 638,047 is: 985,213.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,214 : 638,047 = 638,047 : x
  2. Step 2: Convert to fraction form
    413,214/638,047 = 638,047/x
  3. Step 3: Cross multiply
    413,214x = 638,047 × 638,047
  4. Step 4: Simplify right side
    413,214x = 407,103,974,209
  5. Step 5: Solve for x
    x = 407,103,974,209/413,214
  6. Step 6: Final answer
    x = 985,213.41

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.