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Finding the Fourth Proportional to 460.40, 689.10 and 413.96

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Solution

The fourth proportional to 460.40, 689.10 and 413.96 is: 619.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    460.40 : 689.10 = 413.96 : x
  2. Step 2: Convert to fraction form
    460.40/689.10 = 413.96/x
  3. Step 3: Cross multiply
    460.40x = 689.10 × 413.96
  4. Step 4: Simplify right side
    460.40x = 285,259.84
  5. Step 5: Solve for x
    x = 285,259.84/460.40
  6. Step 6: Final answer
    x = 619.59

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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.