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Finding the Fourth Proportional to 1,029.40, 1,544.26 and 413.12

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Solution

The fourth proportional to 1,029.40, 1,544.26 and 413.12 is: 619.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029.40 : 1,544.26 = 413.12 : x
  2. Step 2: Convert to fraction form
    1,029.40/1,544.26 = 413.12/x
  3. Step 3: Cross multiply
    1,029.40x = 1,544.26 × 413.12
  4. Step 4: Simplify right side
    1,029.40x = 637,964.69
  5. Step 5: Solve for x
    x = 637,964.69/1,029.40
  6. Step 6: Final answer
    x = 619.74

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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.