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Finding the Third Proportional to 83,106 and 177,888

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Solution

The third proportional to 83,106 and 177,888 is: 380,768.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,106 : 177,888 = 177,888 : x
  2. Step 2: Convert to fraction form
    83,106/177,888 = 177,888/x
  3. Step 3: Cross multiply
    83,106x = 177,888 × 177,888
  4. Step 4: Simplify right side
    83,106x = 31,644,140,544
  5. Step 5: Solve for x
    x = 31,644,140,544/83,106
  6. Step 6: Final answer
    x = 380,768.42

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.