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Finding the Third Proportional to 412.03 and 565.73

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Solution

The third proportional to 412.03 and 565.73 is: 776.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.03 : 565.73 = 565.73 : x
  2. Step 2: Convert to fraction form
    412.03/565.73 = 565.73/x
  3. Step 3: Cross multiply
    412.03x = 565.73 × 565.73
  4. Step 4: Simplify right side
    412.03x = 320,055.38
  5. Step 5: Solve for x
    x = 320,055.38/412.03
  6. Step 6: Final answer
    x = 776.77

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.