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Finding the Third Proportional to 305,106 and 461,601

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Solution

The third proportional to 305,106 and 461,601 is: 698,365.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    305,106 : 461,601 = 461,601 : x
  2. Step 2: Convert to fraction form
    305,106/461,601 = 461,601/x
  3. Step 3: Cross multiply
    305,106x = 461,601 × 461,601
  4. Step 4: Simplify right side
    305,106x = 213,075,483,201
  5. Step 5: Solve for x
    x = 213,075,483,201/305,106
  6. Step 6: Final answer
    x = 698,365.43

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.