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Finding the Third Proportional to 413,548 and 561,257

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Solution

The third proportional to 413,548 and 561,257 is: 761,723.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,548 : 561,257 = 561,257 : x
  2. Step 2: Convert to fraction form
    413,548/561,257 = 561,257/x
  3. Step 3: Cross multiply
    413,548x = 561,257 × 561,257
  4. Step 4: Simplify right side
    413,548x = 315,009,420,049
  5. Step 5: Solve for x
    x = 315,009,420,049/413,548
  6. Step 6: Final answer
    x = 761,723.96

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.