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Finding the Fourth Proportional to 1,384.64, 2,077.08 and 410.78

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Solution

The fourth proportional to 1,384.64, 2,077.08 and 410.78 is: 616.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,384.64 : 2,077.08 = 410.78 : x
  2. Step 2: Convert to fraction form
    1,384.64/2,077.08 = 410.78/x
  3. Step 3: Cross multiply
    1,384.64x = 2,077.08 × 410.78
  4. Step 4: Simplify right side
    1,384.64x = 853,222.92
  5. Step 5: Solve for x
    x = 853,222.92/1,384.64
  6. Step 6: Final answer
    x = 616.21

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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.