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Finding the Third Proportional to 409 and 1,034

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Solution

The third proportional to 409 and 1,034 is: 2,614.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 1,034 = 1,034 : x
  2. Step 2: Convert to fraction form
    409/1,034 = 1,034/x
  3. Step 3: Cross multiply
    409x = 1,034 × 1,034
  4. Step 4: Simplify right side
    409x = 1,069,156
  5. Step 5: Solve for x
    x = 1,069,156/409
  6. Step 6: Final answer
    x = 2,614.07

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Why These Related Problems?

These problems maintain the same ratio (2.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.