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Finding the Third Proportional to 102,564 and 219,726

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Solution

The third proportional to 102,564 and 219,726 is: 470,725.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,564 : 219,726 = 219,726 : x
  2. Step 2: Convert to fraction form
    102,564/219,726 = 219,726/x
  3. Step 3: Cross multiply
    102,564x = 219,726 × 219,726
  4. Step 4: Simplify right side
    102,564x = 48,279,515,076
  5. Step 5: Solve for x
    x = 48,279,515,076/102,564
  6. Step 6: Final answer
    x = 470,725.74

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.