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Finding the Fourth Proportional to 1,106.35, 1,658.47 and 412.54

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Solution

The fourth proportional to 1,106.35, 1,658.47 and 412.54 is: 618.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.35 : 1,658.47 = 412.54 : x
  2. Step 2: Convert to fraction form
    1,106.35/1,658.47 = 412.54/x
  3. Step 3: Cross multiply
    1,106.35x = 1,658.47 × 412.54
  4. Step 4: Simplify right side
    1,106.35x = 684,185.21
  5. Step 5: Solve for x
    x = 684,185.21/1,106.35
  6. Step 6: Final answer
    x = 618.42

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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.