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Finding the Third Proportional to 412.38 and 643.57

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Solution

The third proportional to 412.38 and 643.57 is: 1,004.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.38 : 643.57 = 643.57 : x
  2. Step 2: Convert to fraction form
    412.38/643.57 = 643.57/x
  3. Step 3: Cross multiply
    412.38x = 643.57 × 643.57
  4. Step 4: Simplify right side
    412.38x = 414,182.75
  5. Step 5: Solve for x
    x = 414,182.75/412.38
  6. Step 6: Final answer
    x = 1,004.36

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.