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Finding the Third Proportional to 230,078 and 471,310

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Solution

The third proportional to 230,078 and 471,310 is: 965,468.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    230,078 : 471,310 = 471,310 : x
  2. Step 2: Convert to fraction form
    230,078/471,310 = 471,310/x
  3. Step 3: Cross multiply
    230,078x = 471,310 × 471,310
  4. Step 4: Simplify right side
    230,078x = 222,133,116,100
  5. Step 5: Solve for x
    x = 222,133,116,100/230,078
  6. Step 6: Final answer
    x = 965,468.74

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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.