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Finding the Third Proportional to 13,972 and 16,420

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Solution

The third proportional to 13,972 and 16,420 is: 19,296.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,972 : 16,420 = 16,420 : x
  2. Step 2: Convert to fraction form
    13,972/16,420 = 16,420/x
  3. Step 3: Cross multiply
    13,972x = 16,420 × 16,420
  4. Step 4: Simplify right side
    13,972x = 269,616,400
  5. Step 5: Solve for x
    x = 269,616,400/13,972
  6. Step 6: Final answer
    x = 19,296.91

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.