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Finding the Third Proportional to 219,456 and 512,784

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Solution

The third proportional to 219,456 and 512,784 is: 1,198,178.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    219,456 : 512,784 = 512,784 : x
  2. Step 2: Convert to fraction form
    219,456/512,784 = 512,784/x
  3. Step 3: Cross multiply
    219,456x = 512,784 × 512,784
  4. Step 4: Simplify right side
    219,456x = 262,947,430,656
  5. Step 5: Solve for x
    x = 262,947,430,656/219,456
  6. Step 6: Final answer
    x = 1,198,178.36

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.