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Finding the Third Proportional to 205.31 and 322.03

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Solution

The third proportional to 205.31 and 322.03 is: 505.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.31 : 322.03 = 322.03 : x
  2. Step 2: Convert to fraction form
    205.31/322.03 = 322.03/x
  3. Step 3: Cross multiply
    205.31x = 322.03 × 322.03
  4. Step 4: Simplify right side
    205.31x = 103,704.13
  5. Step 5: Solve for x
    x = 103,704.13/205.31
  6. Step 6: Final answer
    x = 505.10

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.