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Finding the Fourth Proportional to 823.76, 1,235.86 and 412.40

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Solution

The fourth proportional to 823.76, 1,235.86 and 412.40 is: 618.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.76 : 1,235.86 = 412.40 : x
  2. Step 2: Convert to fraction form
    823.76/1,235.86 = 412.40/x
  3. Step 3: Cross multiply
    823.76x = 1,235.86 × 412.40
  4. Step 4: Simplify right side
    823.76x = 509,661.45
  5. Step 5: Solve for x
    x = 509,661.45/823.76
  6. Step 6: Final answer
    x = 618.71

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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.