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Finding the Fourth Proportional to 823.57, 1,234.78 and 412.42

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Solution

The fourth proportional to 823.57, 1,234.78 and 412.42 is: 618.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.57 : 1,234.78 = 412.42 : x
  2. Step 2: Convert to fraction form
    823.57/1,234.78 = 412.42/x
  3. Step 3: Cross multiply
    823.57x = 1,234.78 × 412.42
  4. Step 4: Simplify right side
    823.57x = 509,239.73
  5. Step 5: Solve for x
    x = 509,239.73/823.57
  6. Step 6: Final answer
    x = 618.33

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Half scale
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Double scale
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1.5x scale

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.