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Finding the Fourth Proportional to 1,567.64, 2,351.42 and 413.40

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Solution

The fourth proportional to 1,567.64, 2,351.42 and 413.40 is: 620.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,567.64 : 2,351.42 = 413.40 : x
  2. Step 2: Convert to fraction form
    1,567.64/2,351.42 = 413.40/x
  3. Step 3: Cross multiply
    1,567.64x = 2,351.42 × 413.40
  4. Step 4: Simplify right side
    1,567.64x = 972,077.03
  5. Step 5: Solve for x
    x = 972,077.03/1,567.64
  6. Step 6: Final answer
    x = 620.09

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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.