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Finding the Third Proportional to 102,146 and 164,019

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Solution

The third proportional to 102,146 and 164,019 is: 263,370.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,146 : 164,019 = 164,019 : x
  2. Step 2: Convert to fraction form
    102,146/164,019 = 164,019/x
  3. Step 3: Cross multiply
    102,146x = 164,019 × 164,019
  4. Step 4: Simplify right side
    102,146x = 26,902,232,361
  5. Step 5: Solve for x
    x = 26,902,232,361/102,146
  6. Step 6: Final answer
    x = 263,370.39

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.