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Finding the Third Proportional to 413,047 and 631,443

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Solution

The third proportional to 413,047 and 631,443 is: 965,314.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,047 : 631,443 = 631,443 : x
  2. Step 2: Convert to fraction form
    413,047/631,443 = 631,443/x
  3. Step 3: Cross multiply
    413,047x = 631,443 × 631,443
  4. Step 4: Simplify right side
    413,047x = 398,720,262,249
  5. Step 5: Solve for x
    x = 398,720,262,249/413,047
  6. Step 6: Final answer
    x = 965,314.51

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.