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Finding the Third Proportional to 6,814 and 10,416

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Solution

The third proportional to 6,814 and 10,416 is: 15,922.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,814 : 10,416 = 10,416 : x
  2. Step 2: Convert to fraction form
    6,814/10,416 = 10,416/x
  3. Step 3: Cross multiply
    6,814x = 10,416 × 10,416
  4. Step 4: Simplify right side
    6,814x = 108,493,056
  5. Step 5: Solve for x
    x = 108,493,056/6,814
  6. Step 6: Final answer
    x = 15,922.08

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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.