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Finding the Third Proportional to 186.19 and 277.31

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Solution

The third proportional to 186.19 and 277.31 is: 413.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    186.19 : 277.31 = 277.31 : x
  2. Step 2: Convert to fraction form
    186.19/277.31 = 277.31/x
  3. Step 3: Cross multiply
    186.19x = 277.31 × 277.31
  4. Step 4: Simplify right side
    186.19x = 76,902.22
  5. Step 5: Solve for x
    x = 76,902.22/186.19
  6. Step 6: Final answer
    x = 413.04

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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.