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Finding the Fourth Proportional to 470.29, 705.29 and 409.54

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Solution

The fourth proportional to 470.29, 705.29 and 409.54 is: 614.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    470.29 : 705.29 = 409.54 : x
  2. Step 2: Convert to fraction form
    470.29/705.29 = 409.54/x
  3. Step 3: Cross multiply
    470.29x = 705.29 × 409.54
  4. Step 4: Simplify right side
    470.29x = 288,844.47
  5. Step 5: Solve for x
    x = 288,844.47/470.29
  6. Step 6: Final answer
    x = 614.18

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.