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Finding the Third Proportional to 413.44 and 569.53

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Solution

The third proportional to 413.44 and 569.53 is: 784.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    413.44 : 569.53 = 569.53 : x
  2. Step 2: Convert to fraction form
    413.44/569.53 = 569.53/x
  3. Step 3: Cross multiply
    413.44x = 569.53 × 569.53
  4. Step 4: Simplify right side
    413.44x = 324,365.84
  5. Step 5: Solve for x
    x = 324,365.84/413.44
  6. Step 6: Final answer
    x = 784.56

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.