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Finding the Fourth Proportional to 1,105.23, 1,657.84 and 412.07

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Solution

The fourth proportional to 1,105.23, 1,657.84 and 412.07 is: 618.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,105.23 : 1,657.84 = 412.07 : x
  2. Step 2: Convert to fraction form
    1,105.23/1,657.84 = 412.07/x
  3. Step 3: Cross multiply
    1,105.23x = 1,657.84 × 412.07
  4. Step 4: Simplify right side
    1,105.23x = 683,137.84
  5. Step 5: Solve for x
    x = 683,137.84/1,105.23
  6. Step 6: Final answer
    x = 618.10

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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.