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Finding the Third Proportional to 409.75 and 569.75

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Solution

The third proportional to 409.75 and 569.75 is: 792.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.75 : 569.75 = 569.75 : x
  2. Step 2: Convert to fraction form
    409.75/569.75 = 569.75/x
  3. Step 3: Cross multiply
    409.75x = 569.75 × 569.75
  4. Step 4: Simplify right side
    409.75x = 324,615.06
  5. Step 5: Solve for x
    x = 324,615.06/409.75
  6. Step 6: Final answer
    x = 792.23

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.