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Finding the Fourth Proportional to 1,106.07, 1,658.84 and 412.53

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Solution

The fourth proportional to 1,106.07, 1,658.84 and 412.53 is: 618.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.07 : 1,658.84 = 412.53 : x
  2. Step 2: Convert to fraction form
    1,106.07/1,658.84 = 412.53/x
  3. Step 3: Cross multiply
    1,106.07x = 1,658.84 × 412.53
  4. Step 4: Simplify right side
    1,106.07x = 684,319.20
  5. Step 5: Solve for x
    x = 684,319.20/1,106.07
  6. Step 6: Final answer
    x = 618.69

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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.