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Finding the Fourth Proportional to 705.31, 1,057.03 and 413.10

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Solution

The fourth proportional to 705.31, 1,057.03 and 413.10 is: 619.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    705.31 : 1,057.03 = 413.10 : x
  2. Step 2: Convert to fraction form
    705.31/1,057.03 = 413.10/x
  3. Step 3: Cross multiply
    705.31x = 1,057.03 × 413.10
  4. Step 4: Simplify right side
    705.31x = 436,659.09
  5. Step 5: Solve for x
    x = 436,659.09/705.31
  6. Step 6: Final answer
    x = 619.10

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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.