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Finding the Fourth Proportional to 1,097, 1,646.22 and 413

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Solution

The fourth proportional to 1,097, 1,646.22 and 413 is: 619.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,097 : 1,646.22 = 413 : x
  2. Step 2: Convert to fraction form
    1,097/1,646.22 = 413/x
  3. Step 3: Cross multiply
    1,097x = 1,646.22 × 413
  4. Step 4: Simplify right side
    1,097x = 679,888.86
  5. Step 5: Solve for x
    x = 679,888.86/1,097
  6. Step 6: Final answer
    x = 619.77

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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.