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Finding the Third Proportional to 3,206 and 5,776

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Solution

The third proportional to 3,206 and 5,776 is: 10,406.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,206 : 5,776 = 5,776 : x
  2. Step 2: Convert to fraction form
    3,206/5,776 = 5,776/x
  3. Step 3: Cross multiply
    3,206x = 5,776 × 5,776
  4. Step 4: Simplify right side
    3,206x = 33,362,176
  5. Step 5: Solve for x
    x = 33,362,176/3,206
  6. Step 6: Final answer
    x = 10,406.17

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Why These Related Problems?

These problems maintain the same ratio (1.80) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.