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Finding the Fourth Proportional to 1,586, 2,378.97 and 431.75

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Solution

The fourth proportional to 1,586, 2,378.97 and 431.75 is: 647.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,586 : 2,378.97 = 431.75 : x
  2. Step 2: Convert to fraction form
    1,586/2,378.97 = 431.75/x
  3. Step 3: Cross multiply
    1,586x = 2,378.97 × 431.75
  4. Step 4: Simplify right side
    1,586x = 1,027,120.30
  5. Step 5: Solve for x
    x = 1,027,120.30/1,586
  6. Step 6: Final answer
    x = 647.62

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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.