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Finding the Third Proportional to 54,206 and 83,421

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Solution

The third proportional to 54,206 and 83,421 is: 128,381.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,206 : 83,421 = 83,421 : x
  2. Step 2: Convert to fraction form
    54,206/83,421 = 83,421/x
  3. Step 3: Cross multiply
    54,206x = 83,421 × 83,421
  4. Step 4: Simplify right side
    54,206x = 6,959,063,241
  5. Step 5: Solve for x
    x = 6,959,063,241/54,206
  6. Step 6: Final answer
    x = 128,381.79

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.