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Finding the Third Proportional to 209 and 458

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Solution

The third proportional to 209 and 458 is: 1,003.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 458 = 458 : x
  2. Step 2: Convert to fraction form
    209/458 = 458/x
  3. Step 3: Cross multiply
    209x = 458 × 458
  4. Step 4: Simplify right side
    209x = 209,764
  5. Step 5: Solve for x
    x = 209,764/209
  6. Step 6: Final answer
    x = 1,003.66

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.