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Finding the Third Proportional to 189.84 and 289.83

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Solution

The third proportional to 189.84 and 289.83 is: 442.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    189.84 : 289.83 = 289.83 : x
  2. Step 2: Convert to fraction form
    189.84/289.83 = 289.83/x
  3. Step 3: Cross multiply
    189.84x = 289.83 × 289.83
  4. Step 4: Simplify right side
    189.84x = 84,000.34
  5. Step 5: Solve for x
    x = 84,000.34/189.84
  6. Step 6: Final answer
    x = 442.47

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.