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Finding the Fourth Proportional to 705.47, 1,057.86 and 413.07

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Solution

The fourth proportional to 705.47, 1,057.86 and 413.07 is: 619.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    705.47 : 1,057.86 = 413.07 : x
  2. Step 2: Convert to fraction form
    705.47/1,057.86 = 413.07/x
  3. Step 3: Cross multiply
    705.47x = 1,057.86 × 413.07
  4. Step 4: Simplify right side
    705.47x = 436,970.23
  5. Step 5: Solve for x
    x = 436,970.23/705.47
  6. Step 6: Final answer
    x = 619.40

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.