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Finding the Third Proportional to 412.13 and 597.75

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Solution

The third proportional to 412.13 and 597.75 is: 866.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.13 : 597.75 = 597.75 : x
  2. Step 2: Convert to fraction form
    412.13/597.75 = 597.75/x
  3. Step 3: Cross multiply
    412.13x = 597.75 × 597.75
  4. Step 4: Simplify right side
    412.13x = 357,305.06
  5. Step 5: Solve for x
    x = 357,305.06/412.13
  6. Step 6: Final answer
    x = 866.98

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.