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Finding the Third Proportional to 869 and 1,564

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Solution

The third proportional to 869 and 1,564 is: 2,814.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    869 : 1,564 = 1,564 : x
  2. Step 2: Convert to fraction form
    869/1,564 = 1,564/x
  3. Step 3: Cross multiply
    869x = 1,564 × 1,564
  4. Step 4: Simplify right side
    869x = 2,446,096
  5. Step 5: Solve for x
    x = 2,446,096/869
  6. Step 6: Final answer
    x = 2,814.84

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Why These Related Problems?

These problems maintain the same ratio (1.80) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.