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Finding the Third Proportional to 49,082 and 77,842

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Solution

The third proportional to 49,082 and 77,842 is: 123,454.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,082 : 77,842 = 77,842 : x
  2. Step 2: Convert to fraction form
    49,082/77,842 = 77,842/x
  3. Step 3: Cross multiply
    49,082x = 77,842 × 77,842
  4. Step 4: Simplify right side
    49,082x = 6,059,376,964
  5. Step 5: Solve for x
    x = 6,059,376,964/49,082
  6. Step 6: Final answer
    x = 123,454.16

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.