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Finding the Third Proportional to 8,097 and 9,213

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Solution

The third proportional to 8,097 and 9,213 is: 10,482.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,097 : 9,213 = 9,213 : x
  2. Step 2: Convert to fraction form
    8,097/9,213 = 9,213/x
  3. Step 3: Cross multiply
    8,097x = 9,213 × 9,213
  4. Step 4: Simplify right side
    8,097x = 84,879,369
  5. Step 5: Solve for x
    x = 84,879,369/8,097
  6. Step 6: Final answer
    x = 10,482.82

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.