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Finding the Third Proportional to 5,420 and 8,097

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Solution

The third proportional to 5,420 and 8,097 is: 12,096.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,420 : 8,097 = 8,097 : x
  2. Step 2: Convert to fraction form
    5,420/8,097 = 8,097/x
  3. Step 3: Cross multiply
    5,420x = 8,097 × 8,097
  4. Step 4: Simplify right side
    5,420x = 65,561,409
  5. Step 5: Solve for x
    x = 65,561,409/5,420
  6. Step 6: Final answer
    x = 12,096.20

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.