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Finding the Third Proportional to 48,984 and 102,206

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Solution

The third proportional to 48,984 and 102,206 is: 213,254.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    48,984 : 102,206 = 102,206 : x
  2. Step 2: Convert to fraction form
    48,984/102,206 = 102,206/x
  3. Step 3: Cross multiply
    48,984x = 102,206 × 102,206
  4. Step 4: Simplify right side
    48,984x = 10,446,066,436
  5. Step 5: Solve for x
    x = 10,446,066,436/48,984
  6. Step 6: Final answer
    x = 213,254.66

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.