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Finding the Third Proportional to 7,842 and 16,323

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Solution

The third proportional to 7,842 and 16,323 is: 33,976.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,842 : 16,323 = 16,323 : x
  2. Step 2: Convert to fraction form
    7,842/16,323 = 16,323/x
  3. Step 3: Cross multiply
    7,842x = 16,323 × 16,323
  4. Step 4: Simplify right side
    7,842x = 266,440,329
  5. Step 5: Solve for x
    x = 266,440,329/7,842
  6. Step 6: Final answer
    x = 33,976.07

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.