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Finding the Third Proportional to 205,743 and 293,646

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Solution

The third proportional to 205,743 and 293,646 is: 419,105.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,743 : 293,646 = 293,646 : x
  2. Step 2: Convert to fraction form
    205,743/293,646 = 293,646/x
  3. Step 3: Cross multiply
    205,743x = 293,646 × 293,646
  4. Step 4: Simplify right side
    205,743x = 86,227,973,316
  5. Step 5: Solve for x
    x = 86,227,973,316/205,743
  6. Step 6: Final answer
    x = 419,105.26

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.