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Finding the Third Proportional to 830 and 2,057

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Solution

The third proportional to 830 and 2,057 is: 5,097.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    830 : 2,057 = 2,057 : x
  2. Step 2: Convert to fraction form
    830/2,057 = 2,057/x
  3. Step 3: Cross multiply
    830x = 2,057 × 2,057
  4. Step 4: Simplify right side
    830x = 4,231,249
  5. Step 5: Solve for x
    x = 4,231,249/830
  6. Step 6: Final answer
    x = 5,097.89

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Why These Related Problems?

These problems maintain the same ratio (2.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.