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Finding the Third Proportional to 13,970 and 16,400

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Solution

The third proportional to 13,970 and 16,400 is: 19,252.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,970 : 16,400 = 16,400 : x
  2. Step 2: Convert to fraction form
    13,970/16,400 = 16,400/x
  3. Step 3: Cross multiply
    13,970x = 16,400 × 16,400
  4. Step 4: Simplify right side
    13,970x = 268,960,000
  5. Step 5: Solve for x
    x = 268,960,000/13,970
  6. Step 6: Final answer
    x = 19,252.68

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.