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Finding the Third Proportional to 209.25 and 516.38

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Solution

The third proportional to 209.25 and 516.38 is: 1,274.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.25 : 516.38 = 516.38 : x
  2. Step 2: Convert to fraction form
    209.25/516.38 = 516.38/x
  3. Step 3: Cross multiply
    209.25x = 516.38 × 516.38
  4. Step 4: Simplify right side
    209.25x = 266,643.14
  5. Step 5: Solve for x
    x = 266,643.14/209.25
  6. Step 6: Final answer
    x = 1,274.28

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Why These Related Problems?

These problems maintain the same ratio (2.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.