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Finding the Third Proportional to 2,971 and 6,406

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Solution

The third proportional to 2,971 and 6,406 is: 13,812.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,971 : 6,406 = 6,406 : x
  2. Step 2: Convert to fraction form
    2,971/6,406 = 6,406/x
  3. Step 3: Cross multiply
    2,971x = 6,406 × 6,406
  4. Step 4: Simplify right side
    2,971x = 41,036,836
  5. Step 5: Solve for x
    x = 41,036,836/2,971
  6. Step 6: Final answer
    x = 13,812.47

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.