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Finding the Fourth Proportional to 1,106.33, 1,658.34 and 412.56

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Solution

The fourth proportional to 1,106.33, 1,658.34 and 412.56 is: 618.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.33 : 1,658.34 = 412.56 : x
  2. Step 2: Convert to fraction form
    1,106.33/1,658.34 = 412.56/x
  3. Step 3: Cross multiply
    1,106.33x = 1,658.34 × 412.56
  4. Step 4: Simplify right side
    1,106.33x = 684,164.75
  5. Step 5: Solve for x
    x = 684,164.75/1,106.33
  6. Step 6: Final answer
    x = 618.41

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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.