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Finding the Third Proportional to 51,506 and 106,320

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Solution

The third proportional to 51,506 and 106,320 is: 219,468.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,506 : 106,320 = 106,320 : x
  2. Step 2: Convert to fraction form
    51,506/106,320 = 106,320/x
  3. Step 3: Cross multiply
    51,506x = 106,320 × 106,320
  4. Step 4: Simplify right side
    51,506x = 11,303,942,400
  5. Step 5: Solve for x
    x = 11,303,942,400/51,506
  6. Step 6: Final answer
    x = 219,468.46

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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.