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Finding the Third Proportional to 10,405 and 22,537

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Solution

The third proportional to 10,405 and 22,537 is: 48,814.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,405 : 22,537 = 22,537 : x
  2. Step 2: Convert to fraction form
    10,405/22,537 = 22,537/x
  3. Step 3: Cross multiply
    10,405x = 22,537 × 22,537
  4. Step 4: Simplify right side
    10,405x = 507,916,369
  5. Step 5: Solve for x
    x = 507,916,369/10,405
  6. Step 6: Final answer
    x = 48,814.64

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.