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Finding the Third Proportional to 1,977 and 2,185

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Solution

The third proportional to 1,977 and 2,185 is: 2,414.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,977 : 2,185 = 2,185 : x
  2. Step 2: Convert to fraction form
    1,977/2,185 = 2,185/x
  3. Step 3: Cross multiply
    1,977x = 2,185 × 2,185
  4. Step 4: Simplify right side
    1,977x = 4,774,225
  5. Step 5: Solve for x
    x = 4,774,225/1,977
  6. Step 6: Final answer
    x = 2,414.88

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.