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Finding the Third Proportional to 32 and 42.09

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Solution

The third proportional to 32 and 42.09 is: 55.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    32 : 42.09 = 42.09 : x
  2. Step 2: Convert to fraction form
    32/42.09 = 42.09/x
  3. Step 3: Cross multiply
    32x = 42.09 × 42.09
  4. Step 4: Simplify right side
    32x = 1,771.88
  5. Step 5: Solve for x
    x = 1,771.88/32
  6. Step 6: Final answer
    x = 55.37

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.