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Finding the Third Proportional to 384,116 and 509,713

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Solution

The third proportional to 384,116 and 509,713 is: 676,377.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    384,116 : 509,713 = 509,713 : x
  2. Step 2: Convert to fraction form
    384,116/509,713 = 509,713/x
  3. Step 3: Cross multiply
    384,116x = 509,713 × 509,713
  4. Step 4: Simplify right side
    384,116x = 259,807,342,369
  5. Step 5: Solve for x
    x = 259,807,342,369/384,116
  6. Step 6: Final answer
    x = 676,377.30

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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.