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Finding the Third Proportional to 41,764 and 97,822

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Solution

The third proportional to 41,764 and 97,822 is: 229,124.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    41,764 : 97,822 = 97,822 : x
  2. Step 2: Convert to fraction form
    41,764/97,822 = 97,822/x
  3. Step 3: Cross multiply
    41,764x = 97,822 × 97,822
  4. Step 4: Simplify right side
    41,764x = 9,569,143,684
  5. Step 5: Solve for x
    x = 9,569,143,684/41,764
  6. Step 6: Final answer
    x = 229,124.21

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.