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Finding the Third Proportional to 3,872 and 5,724

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Solution

The third proportional to 3,872 and 5,724 is: 8,461.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,872 : 5,724 = 5,724 : x
  2. Step 2: Convert to fraction form
    3,872/5,724 = 5,724/x
  3. Step 3: Cross multiply
    3,872x = 5,724 × 5,724
  4. Step 4: Simplify right side
    3,872x = 32,764,176
  5. Step 5: Solve for x
    x = 32,764,176/3,872
  6. Step 6: Final answer
    x = 8,461.82

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.