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Finding the Fourth Proportional to 1,029, 1,542.89 and 413.00

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Solution

The fourth proportional to 1,029, 1,542.89 and 413.00 is: 619.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029 : 1,542.89 = 413.00 : x
  2. Step 2: Convert to fraction form
    1,029/1,542.89 = 413.00/x
  3. Step 3: Cross multiply
    1,029x = 1,542.89 × 413.00
  4. Step 4: Simplify right side
    1,029x = 637,205.86
  5. Step 5: Solve for x
    x = 637,205.86/1,029
  6. Step 6: Final answer
    x = 619.25

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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.