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Finding the Third Proportional to 382,401 and 824,671

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Solution

The third proportional to 382,401 and 824,671 is: 1,778,453.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    382,401 : 824,671 = 824,671 : x
  2. Step 2: Convert to fraction form
    382,401/824,671 = 824,671/x
  3. Step 3: Cross multiply
    382,401x = 824,671 × 824,671
  4. Step 4: Simplify right side
    382,401x = 680,082,258,241
  5. Step 5: Solve for x
    x = 680,082,258,241/382,401
  6. Step 6: Final answer
    x = 1,778,453.14

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.