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Finding the Third Proportional to 5,416 and 8,164

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Solution

The third proportional to 5,416 and 8,164 is: 12,306.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,416 : 8,164 = 8,164 : x
  2. Step 2: Convert to fraction form
    5,416/8,164 = 8,164/x
  3. Step 3: Cross multiply
    5,416x = 8,164 × 8,164
  4. Step 4: Simplify right side
    5,416x = 66,650,896
  5. Step 5: Solve for x
    x = 66,650,896/5,416
  6. Step 6: Final answer
    x = 12,306.30

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.