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Finding the Third Proportional to 10,584 and 16,213

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Solution

The third proportional to 10,584 and 16,213 is: 24,835.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,584 : 16,213 = 16,213 : x
  2. Step 2: Convert to fraction form
    10,584/16,213 = 16,213/x
  3. Step 3: Cross multiply
    10,584x = 16,213 × 16,213
  4. Step 4: Simplify right side
    10,584x = 262,861,369
  5. Step 5: Solve for x
    x = 262,861,369/10,584
  6. Step 6: Final answer
    x = 24,835.73

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.