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Finding the Third Proportional to 5,984 and 14,416

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Solution

The third proportional to 5,984 and 14,416 is: 34,729.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,984 : 14,416 = 14,416 : x
  2. Step 2: Convert to fraction form
    5,984/14,416 = 14,416/x
  3. Step 3: Cross multiply
    5,984x = 14,416 × 14,416
  4. Step 4: Simplify right side
    5,984x = 207,821,056
  5. Step 5: Solve for x
    x = 207,821,056/5,984
  6. Step 6: Final answer
    x = 34,729.45

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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.