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Finding the Third Proportional to 405.75 and 578.25

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Solution

The third proportional to 405.75 and 578.25 is: 824.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    405.75 : 578.25 = 578.25 : x
  2. Step 2: Convert to fraction form
    405.75/578.25 = 578.25/x
  3. Step 3: Cross multiply
    405.75x = 578.25 × 578.25
  4. Step 4: Simplify right side
    405.75x = 334,373.06
  5. Step 5: Solve for x
    x = 334,373.06/405.75
  6. Step 6: Final answer
    x = 824.09

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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.