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Finding the Third Proportional to 3,006 and 6,409.50

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Solution

The third proportional to 3,006 and 6,409.50 is: 13,666.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,006 : 6,409.50 = 6,409.50 : x
  2. Step 2: Convert to fraction form
    3,006/6,409.50 = 6,409.50/x
  3. Step 3: Cross multiply
    3,006x = 6,409.50 × 6,409.50
  4. Step 4: Simplify right side
    3,006x = 41,081,690.25
  5. Step 5: Solve for x
    x = 41,081,690.25/3,006
  6. Step 6: Final answer
    x = 13,666.56

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.