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Finding the Third Proportional to 30,314 and 65,811

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Solution

The third proportional to 30,314 and 65,811 is: 142,874.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,314 : 65,811 = 65,811 : x
  2. Step 2: Convert to fraction form
    30,314/65,811 = 65,811/x
  3. Step 3: Cross multiply
    30,314x = 65,811 × 65,811
  4. Step 4: Simplify right side
    30,314x = 4,331,087,721
  5. Step 5: Solve for x
    x = 4,331,087,721/30,314
  6. Step 6: Final answer
    x = 142,874.17

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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.