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Finding the Third Proportional to 5,306 and 8,229

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Solution

The third proportional to 5,306 and 8,229 is: 12,762.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,306 : 8,229 = 8,229 : x
  2. Step 2: Convert to fraction form
    5,306/8,229 = 8,229/x
  3. Step 3: Cross multiply
    5,306x = 8,229 × 8,229
  4. Step 4: Simplify right side
    5,306x = 67,716,441
  5. Step 5: Solve for x
    x = 67,716,441/5,306
  6. Step 6: Final answer
    x = 12,762.24

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.