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Finding the Third Proportional to 286 and 409.25

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Solution

The third proportional to 286 and 409.25 is: 585.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    286 : 409.25 = 409.25 : x
  2. Step 2: Convert to fraction form
    286/409.25 = 409.25/x
  3. Step 3: Cross multiply
    286x = 409.25 × 409.25
  4. Step 4: Simplify right side
    286x = 167,485.56
  5. Step 5: Solve for x
    x = 167,485.56/286
  6. Step 6: Final answer
    x = 585.61

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.