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Finding the Third Proportional to 854 and 1,670

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Solution

The third proportional to 854 and 1,670 is: 3,265.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    854 : 1,670 = 1,670 : x
  2. Step 2: Convert to fraction form
    854/1,670 = 1,670/x
  3. Step 3: Cross multiply
    854x = 1,670 × 1,670
  4. Step 4: Simplify right side
    854x = 2,788,900
  5. Step 5: Solve for x
    x = 2,788,900/854
  6. Step 6: Final answer
    x = 3,265.69

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Why These Related Problems?

These problems maintain the same ratio (1.96) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.