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Finding the Third Proportional to 410.75 and 642.38

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Solution

The third proportional to 410.75 and 642.38 is: 1,004.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    410.75 : 642.38 = 642.38 : x
  2. Step 2: Convert to fraction form
    410.75/642.38 = 642.38/x
  3. Step 3: Cross multiply
    410.75x = 642.38 × 642.38
  4. Step 4: Simplify right side
    410.75x = 412,645.64
  5. Step 5: Solve for x
    x = 412,645.64/410.75
  6. Step 6: Final answer
    x = 1,004.62

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.