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Finding the Third Proportional to 419.25 and 785.25

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Solution

The third proportional to 419.25 and 785.25 is: 1,470.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.25 : 785.25 = 785.25 : x
  2. Step 2: Convert to fraction form
    419.25/785.25 = 785.25/x
  3. Step 3: Cross multiply
    419.25x = 785.25 × 785.25
  4. Step 4: Simplify right side
    419.25x = 616,617.56
  5. Step 5: Solve for x
    x = 616,617.56/419.25
  6. Step 6: Final answer
    x = 1,470.76

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.