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Finding the Third Proportional to 307,971 and 460,701

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Solution

The third proportional to 307,971 and 460,701 is: 689,173.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    307,971 : 460,701 = 460,701 : x
  2. Step 2: Convert to fraction form
    307,971/460,701 = 460,701/x
  3. Step 3: Cross multiply
    307,971x = 460,701 × 460,701
  4. Step 4: Simplify right side
    307,971x = 212,245,411,401
  5. Step 5: Solve for x
    x = 212,245,411,401/307,971
  6. Step 6: Final answer
    x = 689,173.37

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.