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Finding the Third Proportional to 180,146 and 269,211

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Solution

The third proportional to 180,146 and 269,211 is: 402,310.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,146 : 269,211 = 269,211 : x
  2. Step 2: Convert to fraction form
    180,146/269,211 = 269,211/x
  3. Step 3: Cross multiply
    180,146x = 269,211 × 269,211
  4. Step 4: Simplify right side
    180,146x = 72,474,562,521
  5. Step 5: Solve for x
    x = 72,474,562,521/180,146
  6. Step 6: Final answer
    x = 402,310.14

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.