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Finding the Fourth Proportional to 413.14, 569.61 and 296.50

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Solution

The fourth proportional to 413.14, 569.61 and 296.50 is: 408.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    413.14 : 569.61 = 296.50 : x
  2. Step 2: Convert to fraction form
    413.14/569.61 = 296.50/x
  3. Step 3: Cross multiply
    413.14x = 569.61 × 296.50
  4. Step 4: Simplify right side
    413.14x = 168,889.37
  5. Step 5: Solve for x
    x = 168,889.37/413.14
  6. Step 6: Final answer
    x = 408.79

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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.