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Finding the Third Proportional to 209.81 and 471.09

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Solution

The third proportional to 209.81 and 471.09 is: 1,057.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.81 : 471.09 = 471.09 : x
  2. Step 2: Convert to fraction form
    209.81/471.09 = 471.09/x
  3. Step 3: Cross multiply
    209.81x = 471.09 × 471.09
  4. Step 4: Simplify right side
    209.81x = 221,929.32
  5. Step 5: Solve for x
    x = 221,929.32/209.81
  6. Step 6: Final answer
    x = 1,057.75

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Why These Related Problems?

These problems maintain the same ratio (2.25) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.