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Finding the Third Proportional to 102,564 and 157,436

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Solution

The third proportional to 102,564 and 157,436 is: 241,664.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,564 : 157,436 = 157,436 : x
  2. Step 2: Convert to fraction form
    102,564/157,436 = 157,436/x
  3. Step 3: Cross multiply
    102,564x = 157,436 × 157,436
  4. Step 4: Simplify right side
    102,564x = 24,786,094,096
  5. Step 5: Solve for x
    x = 24,786,094,096/102,564
  6. Step 6: Final answer
    x = 241,664.66

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.