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Finding the Third Proportional to 117 and 209

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Solution

The third proportional to 117 and 209 is: 373.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    117 : 209 = 209 : x
  2. Step 2: Convert to fraction form
    117/209 = 209/x
  3. Step 3: Cross multiply
    117x = 209 × 209
  4. Step 4: Simplify right side
    117x = 43,681
  5. Step 5: Solve for x
    x = 43,681/117
  6. Step 6: Final answer
    x = 373.34

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Why These Related Problems?

These problems maintain the same ratio (1.79) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.