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Finding the Fourth Proportional to 1,106.40, 1,658.94 and 456.78

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Solution

The fourth proportional to 1,106.40, 1,658.94 and 456.78 is: 684.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.40 : 1,658.94 = 456.78 : x
  2. Step 2: Convert to fraction form
    1,106.40/1,658.94 = 456.78/x
  3. Step 3: Cross multiply
    1,106.40x = 1,658.94 × 456.78
  4. Step 4: Simplify right side
    1,106.40x = 757,770.61
  5. Step 5: Solve for x
    x = 757,770.61/1,106.40
  6. Step 6: Final answer
    x = 684.90

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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.