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Finding the Third Proportional to 5,840 and 14,096

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Solution

The third proportional to 5,840 and 14,096 is: 34,023.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,840 : 14,096 = 14,096 : x
  2. Step 2: Convert to fraction form
    5,840/14,096 = 14,096/x
  3. Step 3: Cross multiply
    5,840x = 14,096 × 14,096
  4. Step 4: Simplify right side
    5,840x = 198,697,216
  5. Step 5: Solve for x
    x = 198,697,216/5,840
  6. Step 6: Final answer
    x = 34,023.50

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.