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Finding the Fourth Proportional to 709.24, 978.54 and 414.40

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Solution

The fourth proportional to 709.24, 978.54 and 414.40 is: 571.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    709.24 : 978.54 = 414.40 : x
  2. Step 2: Convert to fraction form
    709.24/978.54 = 414.40/x
  3. Step 3: Cross multiply
    709.24x = 978.54 × 414.40
  4. Step 4: Simplify right side
    709.24x = 405,506.98
  5. Step 5: Solve for x
    x = 405,506.98/709.24
  6. Step 6: Final answer
    x = 571.75

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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.