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Finding the Third Proportional to 30,786 and 65,784

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Solution

The third proportional to 30,786 and 65,784 is: 140,568.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,786 : 65,784 = 65,784 : x
  2. Step 2: Convert to fraction form
    30,786/65,784 = 65,784/x
  3. Step 3: Cross multiply
    30,786x = 65,784 × 65,784
  4. Step 4: Simplify right side
    30,786x = 4,327,534,656
  5. Step 5: Solve for x
    x = 4,327,534,656/30,786
  6. Step 6: Final answer
    x = 140,568.27

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.