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Finding the Third Proportional to 198,214 and 412,842

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Solution

The third proportional to 198,214 and 412,842 is: 859,871.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,214 : 412,842 = 412,842 : x
  2. Step 2: Convert to fraction form
    198,214/412,842 = 412,842/x
  3. Step 3: Cross multiply
    198,214x = 412,842 × 412,842
  4. Step 4: Simplify right side
    198,214x = 170,438,516,964
  5. Step 5: Solve for x
    x = 170,438,516,964/198,214
  6. Step 6: Final answer
    x = 859,871.23

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.