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Finding the Third Proportional to 310.75 and 822.25

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Solution

The third proportional to 310.75 and 822.25 is: 2,175.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    310.75 : 822.25 = 822.25 : x
  2. Step 2: Convert to fraction form
    310.75/822.25 = 822.25/x
  3. Step 3: Cross multiply
    310.75x = 822.25 × 822.25
  4. Step 4: Simplify right side
    310.75x = 676,095.06
  5. Step 5: Solve for x
    x = 676,095.06/310.75
  6. Step 6: Final answer
    x = 2,175.69

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Why These Related Problems?

These problems maintain the same ratio (2.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.