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Finding the Third Proportional to 10,277 and 22,457

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Solution

The third proportional to 10,277 and 22,457 is: 49,072.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,277 : 22,457 = 22,457 : x
  2. Step 2: Convert to fraction form
    10,277/22,457 = 22,457/x
  3. Step 3: Cross multiply
    10,277x = 22,457 × 22,457
  4. Step 4: Simplify right side
    10,277x = 504,316,849
  5. Step 5: Solve for x
    x = 504,316,849/10,277
  6. Step 6: Final answer
    x = 49,072.38

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.