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Finding the Third Proportional to 1,406 and 2,902

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Solution

The third proportional to 1,406 and 2,902 is: 5,989.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406 : 2,902 = 2,902 : x
  2. Step 2: Convert to fraction form
    1,406/2,902 = 2,902/x
  3. Step 3: Cross multiply
    1,406x = 2,902 × 2,902
  4. Step 4: Simplify right side
    1,406x = 8,421,604
  5. Step 5: Solve for x
    x = 8,421,604/1,406
  6. Step 6: Final answer
    x = 5,989.76

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.