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Finding the Third Proportional to 31.50 and 81.75

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Solution

The third proportional to 31.50 and 81.75 is: 212.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    31.50 : 81.75 = 81.75 : x
  2. Step 2: Convert to fraction form
    31.50/81.75 = 81.75/x
  3. Step 3: Cross multiply
    31.50x = 81.75 × 81.75
  4. Step 4: Simplify right side
    31.50x = 6,683.06
  5. Step 5: Solve for x
    x = 6,683.06/31.50
  6. Step 6: Final answer
    x = 212.16

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Why These Related Problems?

These problems maintain the same ratio (2.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.