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Finding the Fourth Proportional to 1,029.83, 1,543.64 and 413.28

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Solution

The fourth proportional to 1,029.83, 1,543.64 and 413.28 is: 619.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029.83 : 1,543.64 = 413.28 : x
  2. Step 2: Convert to fraction form
    1,029.83/1,543.64 = 413.28/x
  3. Step 3: Cross multiply
    1,029.83x = 1,543.64 × 413.28
  4. Step 4: Simplify right side
    1,029.83x = 637,953.47
  5. Step 5: Solve for x
    x = 637,953.47/1,029.83
  6. Step 6: Final answer
    x = 619.48

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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.