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Finding the Fourth Proportional to 1,023.40, 1,413.08 and 827.80

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Solution

The fourth proportional to 1,023.40, 1,413.08 and 827.80 is: 1,143.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023.40 : 1,413.08 = 827.80 : x
  2. Step 2: Convert to fraction form
    1,023.40/1,413.08 = 827.80/x
  3. Step 3: Cross multiply
    1,023.40x = 1,413.08 × 827.80
  4. Step 4: Simplify right side
    1,023.40x = 1,169,747.62
  5. Step 5: Solve for x
    x = 1,169,747.62/1,023.40
  6. Step 6: Final answer
    x = 1,143.00

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.