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Finding the Third Proportional to 45,471 and 106,205

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Solution

The third proportional to 45,471 and 106,205 is: 248,059.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    45,471 : 106,205 = 106,205 : x
  2. Step 2: Convert to fraction form
    45,471/106,205 = 106,205/x
  3. Step 3: Cross multiply
    45,471x = 106,205 × 106,205
  4. Step 4: Simplify right side
    45,471x = 11,279,502,025
  5. Step 5: Solve for x
    x = 11,279,502,025/45,471
  6. Step 6: Final answer
    x = 248,059.25

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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.