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Finding the Fourth Proportional to 685.16, 945.22 and 409

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Solution

The fourth proportional to 685.16, 945.22 and 409 is: 564.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    685.16 : 945.22 = 409 : x
  2. Step 2: Convert to fraction form
    685.16/945.22 = 409/x
  3. Step 3: Cross multiply
    685.16x = 945.22 × 409
  4. Step 4: Simplify right side
    685.16x = 386,594.98
  5. Step 5: Solve for x
    x = 386,594.98/685.16
  6. Step 6: Final answer
    x = 564.24

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.