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Finding the Fourth Proportional to 824.42, 1,138.14 and 509.78

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Solution

The fourth proportional to 824.42, 1,138.14 and 509.78 is: 703.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    824.42 : 1,138.14 = 509.78 : x
  2. Step 2: Convert to fraction form
    824.42/1,138.14 = 509.78/x
  3. Step 3: Cross multiply
    824.42x = 1,138.14 × 509.78
  4. Step 4: Simplify right side
    824.42x = 580,201.01
  5. Step 5: Solve for x
    x = 580,201.01/824.42
  6. Step 6: Final answer
    x = 703.77

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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.