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Finding the Third Proportional to 102,240 and 217,728

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Solution

The third proportional to 102,240 and 217,728 is: 463,668.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,240 : 217,728 = 217,728 : x
  2. Step 2: Convert to fraction form
    102,240/217,728 = 217,728/x
  3. Step 3: Cross multiply
    102,240x = 217,728 × 217,728
  4. Step 4: Simplify right side
    102,240x = 47,405,481,984
  5. Step 5: Solve for x
    x = 47,405,481,984/102,240
  6. Step 6: Final answer
    x = 463,668.64

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.