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Finding the Third Proportional to 409 and 858

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Solution

The third proportional to 409 and 858 is: 1,799.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 858 = 858 : x
  2. Step 2: Convert to fraction form
    409/858 = 858/x
  3. Step 3: Cross multiply
    409x = 858 × 858
  4. Step 4: Simplify right side
    409x = 736,164
  5. Step 5: Solve for x
    x = 736,164/409
  6. Step 6: Final answer
    x = 1,799.91

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.