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Finding the Third Proportional to 309 and 458

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Solution

The third proportional to 309 and 458 is: 678.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    309 : 458 = 458 : x
  2. Step 2: Convert to fraction form
    309/458 = 458/x
  3. Step 3: Cross multiply
    309x = 458 × 458
  4. Step 4: Simplify right side
    309x = 209,764
  5. Step 5: Solve for x
    x = 209,764/309
  6. Step 6: Final answer
    x = 678.85

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These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.