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Finding the Fourth Proportional to 1,105.10, 1,658.01 and 412.14

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Solution

The fourth proportional to 1,105.10, 1,658.01 and 412.14 is: 618.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,105.10 : 1,658.01 = 412.14 : x
  2. Step 2: Convert to fraction form
    1,105.10/1,658.01 = 412.14/x
  3. Step 3: Cross multiply
    1,105.10x = 1,658.01 × 412.14
  4. Step 4: Simplify right side
    1,105.10x = 683,332.24
  5. Step 5: Solve for x
    x = 683,332.24/1,105.10
  6. Step 6: Final answer
    x = 618.34

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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.