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Finding the Fourth Proportional to 4,097, 5,653.86 and 2,234

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Solution

The fourth proportional to 4,097, 5,653.86 and 2,234 is: 3,082.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,097 : 5,653.86 = 2,234 : x
  2. Step 2: Convert to fraction form
    4,097/5,653.86 = 2,234/x
  3. Step 3: Cross multiply
    4,097x = 5,653.86 × 2,234
  4. Step 4: Simplify right side
    4,097x = 12,630,723.24
  5. Step 5: Solve for x
    x = 12,630,723.24/4,097
  6. Step 6: Final answer
    x = 3,082.92

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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.