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Finding the Third Proportional to 461 and 973

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Solution

The third proportional to 461 and 973 is: 2,053.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    461 : 973 = 973 : x
  2. Step 2: Convert to fraction form
    461/973 = 973/x
  3. Step 3: Cross multiply
    461x = 973 × 973
  4. Step 4: Simplify right side
    461x = 946,729
  5. Step 5: Solve for x
    x = 946,729/461
  6. Step 6: Final answer
    x = 2,053.64

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.