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Finding the Third Proportional to 6,417 and 7,821

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Solution

The third proportional to 6,417 and 7,821 is: 9,532.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,417 : 7,821 = 7,821 : x
  2. Step 2: Convert to fraction form
    6,417/7,821 = 7,821/x
  3. Step 3: Cross multiply
    6,417x = 7,821 × 7,821
  4. Step 4: Simplify right side
    6,417x = 61,168,041
  5. Step 5: Solve for x
    x = 61,168,041/6,417
  6. Step 6: Final answer
    x = 9,532.19

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.