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Finding the Third Proportional to 5,972 and 14,056

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Solution

The third proportional to 5,972 and 14,056 is: 33,082.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,972 : 14,056 = 14,056 : x
  2. Step 2: Convert to fraction form
    5,972/14,056 = 14,056/x
  3. Step 3: Cross multiply
    5,972x = 14,056 × 14,056
  4. Step 4: Simplify right side
    5,972x = 197,571,136
  5. Step 5: Solve for x
    x = 197,571,136/5,972
  6. Step 6: Final answer
    x = 33,082.91

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.