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Finding the Third Proportional to 7,740 and 16,400

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Solution

The third proportional to 7,740 and 16,400 is: 34,749.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,740 : 16,400 = 16,400 : x
  2. Step 2: Convert to fraction form
    7,740/16,400 = 16,400/x
  3. Step 3: Cross multiply
    7,740x = 16,400 × 16,400
  4. Step 4: Simplify right side
    7,740x = 268,960,000
  5. Step 5: Solve for x
    x = 268,960,000/7,740
  6. Step 6: Final answer
    x = 34,749.35

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.