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Finding the Fourth Proportional to 1,077.67, 1,616.09 and 419.46

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Solution

The fourth proportional to 1,077.67, 1,616.09 and 419.46 is: 629.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,077.67 : 1,616.09 = 419.46 : x
  2. Step 2: Convert to fraction form
    1,077.67/1,616.09 = 419.46/x
  3. Step 3: Cross multiply
    1,077.67x = 1,616.09 × 419.46
  4. Step 4: Simplify right side
    1,077.67x = 677,876.95
  5. Step 5: Solve for x
    x = 677,876.95/1,077.67
  6. Step 6: Final answer
    x = 629.02

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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.