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Finding the Third Proportional to 384,115 and 509,712

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Solution

The third proportional to 384,115 and 509,712 is: 676,376.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    384,115 : 509,712 = 509,712 : x
  2. Step 2: Convert to fraction form
    384,115/509,712 = 509,712/x
  3. Step 3: Cross multiply
    384,115x = 509,712 × 509,712
  4. Step 4: Simplify right side
    384,115x = 259,806,322,944
  5. Step 5: Solve for x
    x = 259,806,322,944/384,115
  6. Step 6: Final answer
    x = 676,376.41

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.