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Finding the Fourth Proportional to 586.64, 809.85 and 409.76

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Solution

The fourth proportional to 586.64, 809.85 and 409.76 is: 565.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    586.64 : 809.85 = 409.76 : x
  2. Step 2: Convert to fraction form
    586.64/809.85 = 409.76/x
  3. Step 3: Cross multiply
    586.64x = 809.85 × 409.76
  4. Step 4: Simplify right side
    586.64x = 331,840.09
  5. Step 5: Solve for x
    x = 331,840.09/586.64
  6. Step 6: Final answer
    x = 565.67

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.