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Finding the Third Proportional to 409.13 and 677.06

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Solution

The third proportional to 409.13 and 677.06 is: 1,120.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.13 : 677.06 = 677.06 : x
  2. Step 2: Convert to fraction form
    409.13/677.06 = 677.06/x
  3. Step 3: Cross multiply
    409.13x = 677.06 × 677.06
  4. Step 4: Simplify right side
    409.13x = 458,413.63
  5. Step 5: Solve for x
    x = 458,413.63/409.13
  6. Step 6: Final answer
    x = 1,120.47

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.