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Finding the Fourth Proportional to 1,234.74, 1,852.34 and 413.10

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Solution

The fourth proportional to 1,234.74, 1,852.34 and 413.10 is: 619.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,234.74 : 1,852.34 = 413.10 : x
  2. Step 2: Convert to fraction form
    1,234.74/1,852.34 = 413.10/x
  3. Step 3: Cross multiply
    1,234.74x = 1,852.34 × 413.10
  4. Step 4: Simplify right side
    1,234.74x = 765,199.59
  5. Step 5: Solve for x
    x = 765,199.59/1,234.74
  6. Step 6: Final answer
    x = 619.72

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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.