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Finding the Third Proportional to 4,100 and 7,784

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Solution

The third proportional to 4,100 and 7,784 is: 14,778.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,100 : 7,784 = 7,784 : x
  2. Step 2: Convert to fraction form
    4,100/7,784 = 7,784/x
  3. Step 3: Cross multiply
    4,100x = 7,784 × 7,784
  4. Step 4: Simplify right side
    4,100x = 60,590,656
  5. Step 5: Solve for x
    x = 60,590,656/4,100
  6. Step 6: Final answer
    x = 14,778.21

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Why These Related Problems?

These problems maintain the same ratio (1.90) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.