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Finding the Third Proportional to 2,971 and 6,499

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Solution

The third proportional to 2,971 and 6,499 is: 14,216.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,971 : 6,499 = 6,499 : x
  2. Step 2: Convert to fraction form
    2,971/6,499 = 6,499/x
  3. Step 3: Cross multiply
    2,971x = 6,499 × 6,499
  4. Step 4: Simplify right side
    2,971x = 42,237,001
  5. Step 5: Solve for x
    x = 42,237,001/2,971
  6. Step 6: Final answer
    x = 14,216.43

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.