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Finding the Third Proportional to 8,142 and 11,646

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Solution

The third proportional to 8,142 and 11,646 is: 16,657.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,142 : 11,646 = 11,646 : x
  2. Step 2: Convert to fraction form
    8,142/11,646 = 11,646/x
  3. Step 3: Cross multiply
    8,142x = 11,646 × 11,646
  4. Step 4: Simplify right side
    8,142x = 135,629,316
  5. Step 5: Solve for x
    x = 135,629,316/8,142
  6. Step 6: Final answer
    x = 16,657.99

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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.