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Finding the Third Proportional to 5,840 and 8,364

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Solution

The third proportional to 5,840 and 8,364 is: 11,978.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,840 : 8,364 = 8,364 : x
  2. Step 2: Convert to fraction form
    5,840/8,364 = 8,364/x
  3. Step 3: Cross multiply
    5,840x = 8,364 × 8,364
  4. Step 4: Simplify right side
    5,840x = 69,956,496
  5. Step 5: Solve for x
    x = 69,956,496/5,840
  6. Step 6: Final answer
    x = 11,978.85

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.