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Finding the Third Proportional to 314,214 and 678,234

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Solution

The third proportional to 314,214 and 678,234 is: 1,463,974.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    314,214 : 678,234 = 678,234 : x
  2. Step 2: Convert to fraction form
    314,214/678,234 = 678,234/x
  3. Step 3: Cross multiply
    314,214x = 678,234 × 678,234
  4. Step 4: Simplify right side
    314,214x = 460,001,358,756
  5. Step 5: Solve for x
    x = 460,001,358,756/314,214
  6. Step 6: Final answer
    x = 1,463,974.74

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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.