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Finding the Third Proportional to 205.74 and 320.01

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Solution

The third proportional to 205.74 and 320.01 is: 497.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.74 : 320.01 = 320.01 : x
  2. Step 2: Convert to fraction form
    205.74/320.01 = 320.01/x
  3. Step 3: Cross multiply
    205.74x = 320.01 × 320.01
  4. Step 4: Simplify right side
    205.74x = 102,403.44
  5. Step 5: Solve for x
    x = 102,403.44/205.74
  6. Step 6: Final answer
    x = 497.72

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.