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Finding the Third Proportional to 23 and 31

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Solution

The third proportional to 23 and 31 is: 41.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    23 : 31 = 31 : x
  2. Step 2: Convert to fraction form
    23/31 = 31/x
  3. Step 3: Cross multiply
    23x = 31 × 31
  4. Step 4: Simplify right side
    23x = 961
  5. Step 5: Solve for x
    x = 961/23
  6. Step 6: Final answer
    x = 41.78

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.