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Finding the Fourth Proportional to 1,025.85, 1,538.42 and 409.77

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Solution

The fourth proportional to 1,025.85, 1,538.42 and 409.77 is: 614.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,025.85 : 1,538.42 = 409.77 : x
  2. Step 2: Convert to fraction form
    1,025.85/1,538.42 = 409.77/x
  3. Step 3: Cross multiply
    1,025.85x = 1,538.42 × 409.77
  4. Step 4: Simplify right side
    1,025.85x = 630,396.31
  5. Step 5: Solve for x
    x = 630,396.31/1,025.85
  6. Step 6: Final answer
    x = 614.51

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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.