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Finding the Third Proportional to 5,724 and 8,166

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Solution

The third proportional to 5,724 and 8,166 is: 11,649.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,724 : 8,166 = 8,166 : x
  2. Step 2: Convert to fraction form
    5,724/8,166 = 8,166/x
  3. Step 3: Cross multiply
    5,724x = 8,166 × 8,166
  4. Step 4: Simplify right side
    5,724x = 66,683,556
  5. Step 5: Solve for x
    x = 66,683,556/5,724
  6. Step 6: Final answer
    x = 11,649.82

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.