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Finding the Third Proportional to 29,961 and 65,207

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Solution

The third proportional to 29,961 and 65,207 is: 141,916.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    29,961 : 65,207 = 65,207 : x
  2. Step 2: Convert to fraction form
    29,961/65,207 = 65,207/x
  3. Step 3: Cross multiply
    29,961x = 65,207 × 65,207
  4. Step 4: Simplify right side
    29,961x = 4,251,952,849
  5. Step 5: Solve for x
    x = 4,251,952,849/29,961
  6. Step 6: Final answer
    x = 141,916.25

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.