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Finding the Third Proportional to 31,920 and 49,824

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Solution

The third proportional to 31,920 and 49,824 is: 77,770.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,920 : 49,824 = 49,824 : x
  2. Step 2: Convert to fraction form
    31,920/49,824 = 49,824/x
  3. Step 3: Cross multiply
    31,920x = 49,824 × 49,824
  4. Step 4: Simplify right side
    31,920x = 2,482,430,976
  5. Step 5: Solve for x
    x = 2,482,430,976/31,920
  6. Step 6: Final answer
    x = 77,770.39

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.