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Finding the Third Proportional to 106,688 and 177,824

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Solution

The third proportional to 106,688 and 177,824 is: 296,391.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,688 : 177,824 = 177,824 : x
  2. Step 2: Convert to fraction form
    106,688/177,824 = 177,824/x
  3. Step 3: Cross multiply
    106,688x = 177,824 × 177,824
  4. Step 4: Simplify right side
    106,688x = 31,621,374,976
  5. Step 5: Solve for x
    x = 31,621,374,976/106,688
  6. Step 6: Final answer
    x = 296,391.11

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.