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Finding the Third Proportional to 157 and 209

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Solution

The third proportional to 157 and 209 is: 278.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    157 : 209 = 209 : x
  2. Step 2: Convert to fraction form
    157/209 = 209/x
  3. Step 3: Cross multiply
    157x = 209 × 209
  4. Step 4: Simplify right side
    157x = 43,681
  5. Step 5: Solve for x
    x = 43,681/157
  6. Step 6: Final answer
    x = 278.22

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.