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Finding the Third Proportional to 193,120 and 409,424

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Solution

The third proportional to 193,120 and 409,424 is: 867,999.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    193,120 : 409,424 = 409,424 : x
  2. Step 2: Convert to fraction form
    193,120/409,424 = 409,424/x
  3. Step 3: Cross multiply
    193,120x = 409,424 × 409,424
  4. Step 4: Simplify right side
    193,120x = 167,628,011,776
  5. Step 5: Solve for x
    x = 167,628,011,776/193,120
  6. Step 6: Final answer
    x = 867,999.23

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.