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Finding the Third Proportional to 5,178 and 10,523

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Solution

The third proportional to 5,178 and 10,523 is: 21,385.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,178 : 10,523 = 10,523 : x
  2. Step 2: Convert to fraction form
    5,178/10,523 = 10,523/x
  3. Step 3: Cross multiply
    5,178x = 10,523 × 10,523
  4. Step 4: Simplify right side
    5,178x = 110,733,529
  5. Step 5: Solve for x
    x = 110,733,529/5,178
  6. Step 6: Final answer
    x = 21,385.39

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.