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Finding the Third Proportional to 258.75 and 284.25

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Solution

The third proportional to 258.75 and 284.25 is: 312.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    258.75 : 284.25 = 284.25 : x
  2. Step 2: Convert to fraction form
    258.75/284.25 = 284.25/x
  3. Step 3: Cross multiply
    258.75x = 284.25 × 284.25
  4. Step 4: Simplify right side
    258.75x = 80,798.06
  5. Step 5: Solve for x
    x = 80,798.06/258.75
  6. Step 6: Final answer
    x = 312.26

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.