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Finding the Third Proportional to 384,113 and 509,709

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Solution

The third proportional to 384,113 and 509,709 is: 676,371.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    384,113 : 509,709 = 509,709 : x
  2. Step 2: Convert to fraction form
    384,113/509,709 = 509,709/x
  3. Step 3: Cross multiply
    384,113x = 509,709 × 509,709
  4. Step 4: Simplify right side
    384,113x = 259,803,264,681
  5. Step 5: Solve for x
    x = 259,803,264,681/384,113
  6. Step 6: Final answer
    x = 676,371.97

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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.