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Finding the Third Proportional to 196,507 and 296,414

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Solution

The third proportional to 196,507 and 296,414 is: 447,115.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    196,507 : 296,414 = 296,414 : x
  2. Step 2: Convert to fraction form
    196,507/296,414 = 296,414/x
  3. Step 3: Cross multiply
    196,507x = 296,414 × 296,414
  4. Step 4: Simplify right side
    196,507x = 87,861,259,396
  5. Step 5: Solve for x
    x = 87,861,259,396/196,507
  6. Step 6: Final answer
    x = 447,115.16

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.