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Finding the Third Proportional to 825 and 1,377

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Solution

The third proportional to 825 and 1,377 is: 2,298.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    825 : 1,377 = 1,377 : x
  2. Step 2: Convert to fraction form
    825/1,377 = 1,377/x
  3. Step 3: Cross multiply
    825x = 1,377 × 1,377
  4. Step 4: Simplify right side
    825x = 1,896,129
  5. Step 5: Solve for x
    x = 1,896,129/825
  6. Step 6: Final answer
    x = 2,298.34

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.