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Finding the Third Proportional to 5,940 and 7,821

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Solution

The third proportional to 5,940 and 7,821 is: 10,297.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,940 : 7,821 = 7,821 : x
  2. Step 2: Convert to fraction form
    5,940/7,821 = 7,821/x
  3. Step 3: Cross multiply
    5,940x = 7,821 × 7,821
  4. Step 4: Simplify right side
    5,940x = 61,168,041
  5. Step 5: Solve for x
    x = 61,168,041/5,940
  6. Step 6: Final answer
    x = 10,297.65

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.