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Finding the Third Proportional to 106,461 and 233,658

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Solution

The third proportional to 106,461 and 233,658 is: 512,826.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,461 : 233,658 = 233,658 : x
  2. Step 2: Convert to fraction form
    106,461/233,658 = 233,658/x
  3. Step 3: Cross multiply
    106,461x = 233,658 × 233,658
  4. Step 4: Simplify right side
    106,461x = 54,596,060,964
  5. Step 5: Solve for x
    x = 54,596,060,964/106,461
  6. Step 6: Final answer
    x = 512,826.87

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.