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Finding the Third Proportional to 414 and 597

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Solution

The third proportional to 414 and 597 is: 860.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 597 = 597 : x
  2. Step 2: Convert to fraction form
    414/597 = 597/x
  3. Step 3: Cross multiply
    414x = 597 × 597
  4. Step 4: Simplify right side
    414x = 356,409
  5. Step 5: Solve for x
    x = 356,409/414
  6. Step 6: Final answer
    x = 860.89

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.