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Finding the Fourth Proportional to 1,106.57, 1,659.42 and 413.08

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Solution

The fourth proportional to 1,106.57, 1,659.42 and 413.08 is: 619.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.57 : 1,659.42 = 413.08 : x
  2. Step 2: Convert to fraction form
    1,106.57/1,659.42 = 413.08/x
  3. Step 3: Cross multiply
    1,106.57x = 1,659.42 × 413.08
  4. Step 4: Simplify right side
    1,106.57x = 685,473.21
  5. Step 5: Solve for x
    x = 685,473.21/1,106.57
  6. Step 6: Final answer
    x = 619.46

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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.