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Finding the Third Proportional to 7,712 and 16,184

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Solution

The third proportional to 7,712 and 16,184 is: 33,962.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,712 : 16,184 = 16,184 : x
  2. Step 2: Convert to fraction form
    7,712/16,184 = 16,184/x
  3. Step 3: Cross multiply
    7,712x = 16,184 × 16,184
  4. Step 4: Simplify right side
    7,712x = 261,921,856
  5. Step 5: Solve for x
    x = 261,921,856/7,712
  6. Step 6: Final answer
    x = 33,962.90

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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.