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Finding the Third Proportional to 106,514 and 232,712

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Solution

The third proportional to 106,514 and 232,712 is: 508,429.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,514 : 232,712 = 232,712 : x
  2. Step 2: Convert to fraction form
    106,514/232,712 = 232,712/x
  3. Step 3: Cross multiply
    106,514x = 232,712 × 232,712
  4. Step 4: Simplify right side
    106,514x = 54,154,874,944
  5. Step 5: Solve for x
    x = 54,154,874,944/106,514
  6. Step 6: Final answer
    x = 508,429.64

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.