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Finding the Third Proportional to 65,834 and 144,169

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Solution

The third proportional to 65,834 and 144,169 is: 315,713.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,834 : 144,169 = 144,169 : x
  2. Step 2: Convert to fraction form
    65,834/144,169 = 144,169/x
  3. Step 3: Cross multiply
    65,834x = 144,169 × 144,169
  4. Step 4: Simplify right side
    65,834x = 20,784,700,561
  5. Step 5: Solve for x
    x = 20,784,700,561/65,834
  6. Step 6: Final answer
    x = 315,713.77

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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.