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Finding the Third Proportional to 160.78 and 209.06

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Solution

The third proportional to 160.78 and 209.06 is: 271.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    160.78 : 209.06 = 209.06 : x
  2. Step 2: Convert to fraction form
    160.78/209.06 = 209.06/x
  3. Step 3: Cross multiply
    160.78x = 209.06 × 209.06
  4. Step 4: Simplify right side
    160.78x = 43,707.13
  5. Step 5: Solve for x
    x = 43,707.13/160.78
  6. Step 6: Final answer
    x = 271.84

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.