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Finding the Third Proportional to 421.75 and 683.25

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Solution

The third proportional to 421.75 and 683.25 is: 1,106.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    421.75 : 683.25 = 683.25 : x
  2. Step 2: Convert to fraction form
    421.75/683.25 = 683.25/x
  3. Step 3: Cross multiply
    421.75x = 683.25 × 683.25
  4. Step 4: Simplify right side
    421.75x = 466,830.56
  5. Step 5: Solve for x
    x = 466,830.56/421.75
  6. Step 6: Final answer
    x = 1,106.89

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Why These Related Problems?

These problems maintain the same ratio (1.62) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.