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Finding the Third Proportional to 230,082 and 471,324

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Solution

The third proportional to 230,082 and 471,324 is: 965,509.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    230,082 : 471,324 = 471,324 : x
  2. Step 2: Convert to fraction form
    230,082/471,324 = 471,324/x
  3. Step 3: Cross multiply
    230,082x = 471,324 × 471,324
  4. Step 4: Simplify right side
    230,082x = 222,146,312,976
  5. Step 5: Solve for x
    x = 222,146,312,976/230,082
  6. Step 6: Final answer
    x = 965,509.31

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.