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Finding the Fourth Proportional to 1,029.61, 1,543.78 and 413.20

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Solution

The fourth proportional to 1,029.61, 1,543.78 and 413.20 is: 619.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029.61 : 1,543.78 = 413.20 : x
  2. Step 2: Convert to fraction form
    1,029.61/1,543.78 = 413.20/x
  3. Step 3: Cross multiply
    1,029.61x = 1,543.78 × 413.20
  4. Step 4: Simplify right side
    1,029.61x = 637,889.90
  5. Step 5: Solve for x
    x = 637,889.90/1,029.61
  6. Step 6: Final answer
    x = 619.55

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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.