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Finding the Third Proportional to 196,214 and 410,194

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Solution

The third proportional to 196,214 and 410,194 is: 857,528.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    196,214 : 410,194 = 410,194 : x
  2. Step 2: Convert to fraction form
    196,214/410,194 = 410,194/x
  3. Step 3: Cross multiply
    196,214x = 410,194 × 410,194
  4. Step 4: Simplify right side
    196,214x = 168,259,117,636
  5. Step 5: Solve for x
    x = 168,259,117,636/196,214
  6. Step 6: Final answer
    x = 857,528.60

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.