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Finding the Third Proportional to 854 and 1,567

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Solution

The third proportional to 854 and 1,567 is: 2,875.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    854 : 1,567 = 1,567 : x
  2. Step 2: Convert to fraction form
    854/1,567 = 1,567/x
  3. Step 3: Cross multiply
    854x = 1,567 × 1,567
  4. Step 4: Simplify right side
    854x = 2,455,489
  5. Step 5: Solve for x
    x = 2,455,489/854
  6. Step 6: Final answer
    x = 2,875.28

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Why These Related Problems?

These problems maintain the same ratio (1.83) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.