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Finding the Third Proportional to 2,123 and 3,185

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Solution

The third proportional to 2,123 and 3,185 is: 4,778.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,123 : 3,185 = 3,185 : x
  2. Step 2: Convert to fraction form
    2,123/3,185 = 3,185/x
  3. Step 3: Cross multiply
    2,123x = 3,185 × 3,185
  4. Step 4: Simplify right side
    2,123x = 10,144,225
  5. Step 5: Solve for x
    x = 10,144,225/2,123
  6. Step 6: Final answer
    x = 4,778.25

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.