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Finding the Third Proportional to 7,784 and 16,270

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Solution

The third proportional to 7,784 and 16,270 is: 34,007.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,784 : 16,270 = 16,270 : x
  2. Step 2: Convert to fraction form
    7,784/16,270 = 16,270/x
  3. Step 3: Cross multiply
    7,784x = 16,270 × 16,270
  4. Step 4: Simplify right side
    7,784x = 264,712,900
  5. Step 5: Solve for x
    x = 264,712,900/7,784
  6. Step 6: Final answer
    x = 34,007.31

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.