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Finding the Third Proportional to 83 and 162.25

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Solution

The third proportional to 83 and 162.25 is: 317.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    83 : 162.25 = 162.25 : x
  2. Step 2: Convert to fraction form
    83/162.25 = 162.25/x
  3. Step 3: Cross multiply
    83x = 162.25 × 162.25
  4. Step 4: Simplify right side
    83x = 26,325.06
  5. Step 5: Solve for x
    x = 26,325.06/83
  6. Step 6: Final answer
    x = 317.17

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.