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Finding the Third Proportional to 31.78 and 51.19

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Solution

The third proportional to 31.78 and 51.19 is: 82.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    31.78 : 51.19 = 51.19 : x
  2. Step 2: Convert to fraction form
    31.78/51.19 = 51.19/x
  3. Step 3: Cross multiply
    31.78x = 51.19 × 51.19
  4. Step 4: Simplify right side
    31.78x = 2,620.16
  5. Step 5: Solve for x
    x = 2,620.16/31.78
  6. Step 6: Final answer
    x = 82.44

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.