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Finding the Third Proportional to 9,777 and 13,971

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Solution

The third proportional to 9,777 and 13,971 is: 19,964.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,777 : 13,971 = 13,971 : x
  2. Step 2: Convert to fraction form
    9,777/13,971 = 13,971/x
  3. Step 3: Cross multiply
    9,777x = 13,971 × 13,971
  4. Step 4: Simplify right side
    9,777x = 195,188,841
  5. Step 5: Solve for x
    x = 195,188,841/9,777
  6. Step 6: Final answer
    x = 19,964.08

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.