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Finding the Third Proportional to 12,031 and 16,057

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Solution

The third proportional to 12,031 and 16,057 is: 21,430.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,031 : 16,057 = 16,057 : x
  2. Step 2: Convert to fraction form
    12,031/16,057 = 16,057/x
  3. Step 3: Cross multiply
    12,031x = 16,057 × 16,057
  4. Step 4: Simplify right side
    12,031x = 257,827,249
  5. Step 5: Solve for x
    x = 257,827,249/12,031
  6. Step 6: Final answer
    x = 21,430.24

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.