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Finding the Third Proportional to 2,309 and 4,096

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Solution

The third proportional to 2,309 and 4,096 is: 7,266.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,309 : 4,096 = 4,096 : x
  2. Step 2: Convert to fraction form
    2,309/4,096 = 4,096/x
  3. Step 3: Cross multiply
    2,309x = 4,096 × 4,096
  4. Step 4: Simplify right side
    2,309x = 16,777,216
  5. Step 5: Solve for x
    x = 16,777,216/2,309
  6. Step 6: Final answer
    x = 7,266.01

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.