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Finding the Third Proportional to 2,178 and 3,729

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Solution

The third proportional to 2,178 and 3,729 is: 6,384.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,178 : 3,729 = 3,729 : x
  2. Step 2: Convert to fraction form
    2,178/3,729 = 3,729/x
  3. Step 3: Cross multiply
    2,178x = 3,729 × 3,729
  4. Step 4: Simplify right side
    2,178x = 13,905,441
  5. Step 5: Solve for x
    x = 13,905,441/2,178
  6. Step 6: Final answer
    x = 6,384.50

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Why These Related Problems?

These problems maintain the same ratio (1.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.