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Finding the Third Proportional to 7,684 and 16,142

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Solution

The third proportional to 7,684 and 16,142 is: 33,909.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,684 : 16,142 = 16,142 : x
  2. Step 2: Convert to fraction form
    7,684/16,142 = 16,142/x
  3. Step 3: Cross multiply
    7,684x = 16,142 × 16,142
  4. Step 4: Simplify right side
    7,684x = 260,564,164
  5. Step 5: Solve for x
    x = 260,564,164/7,684
  6. Step 6: Final answer
    x = 33,909.96

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.