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Finding the Third Proportional to 53,419 and 83,042

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Solution

The third proportional to 53,419 and 83,042 is: 129,092.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,419 : 83,042 = 83,042 : x
  2. Step 2: Convert to fraction form
    53,419/83,042 = 83,042/x
  3. Step 3: Cross multiply
    53,419x = 83,042 × 83,042
  4. Step 4: Simplify right side
    53,419x = 6,895,973,764
  5. Step 5: Solve for x
    x = 6,895,973,764/53,419
  6. Step 6: Final answer
    x = 129,092.15

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.