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Finding the Third Proportional to 51,506 and 106,321

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Solution

The third proportional to 51,506 and 106,321 is: 219,472.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,506 : 106,321 = 106,321 : x
  2. Step 2: Convert to fraction form
    51,506/106,321 = 106,321/x
  3. Step 3: Cross multiply
    51,506x = 106,321 × 106,321
  4. Step 4: Simplify right side
    51,506x = 11,304,155,041
  5. Step 5: Solve for x
    x = 11,304,155,041/51,506
  6. Step 6: Final answer
    x = 219,472.59

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.