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Finding the Third Proportional to 419.25 and 969.75

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Solution

The third proportional to 419.25 and 969.75 is: 2,243.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.25 : 969.75 = 969.75 : x
  2. Step 2: Convert to fraction form
    419.25/969.75 = 969.75/x
  3. Step 3: Cross multiply
    419.25x = 969.75 × 969.75
  4. Step 4: Simplify right side
    419.25x = 940,415.06
  5. Step 5: Solve for x
    x = 940,415.06/419.25
  6. Step 6: Final answer
    x = 2,243.09

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.