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Finding the Third Proportional to 6,501 and 7,851

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Solution

The third proportional to 6,501 and 7,851 is: 9,481.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,501 : 7,851 = 7,851 : x
  2. Step 2: Convert to fraction form
    6,501/7,851 = 7,851/x
  3. Step 3: Cross multiply
    6,501x = 7,851 × 7,851
  4. Step 4: Simplify right side
    6,501x = 61,638,201
  5. Step 5: Solve for x
    x = 61,638,201/6,501
  6. Step 6: Final answer
    x = 9,481.34

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.