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Finding the Third Proportional to 30,824 and 47,821

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Solution

The third proportional to 30,824 and 47,821 is: 74,190.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,824 : 47,821 = 47,821 : x
  2. Step 2: Convert to fraction form
    30,824/47,821 = 47,821/x
  3. Step 3: Cross multiply
    30,824x = 47,821 × 47,821
  4. Step 4: Simplify right side
    30,824x = 2,286,848,041
  5. Step 5: Solve for x
    x = 2,286,848,041/30,824
  6. Step 6: Final answer
    x = 74,190.50

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.