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Finding the Third Proportional to 364,343 and 509,491

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Solution

The third proportional to 364,343 and 509,491 is: 712,463.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    364,343 : 509,491 = 509,491 : x
  2. Step 2: Convert to fraction form
    364,343/509,491 = 509,491/x
  3. Step 3: Cross multiply
    364,343x = 509,491 × 509,491
  4. Step 4: Simplify right side
    364,343x = 259,581,079,081
  5. Step 5: Solve for x
    x = 259,581,079,081/364,343
  6. Step 6: Final answer
    x = 712,463.47

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.