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Finding the Fourth Proportional to 514.40, 709.56 and 416

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Solution

The fourth proportional to 514.40, 709.56 and 416 is: 573.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    514.40 : 709.56 = 416 : x
  2. Step 2: Convert to fraction form
    514.40/709.56 = 416/x
  3. Step 3: Cross multiply
    514.40x = 709.56 × 416
  4. Step 4: Simplify right side
    514.40x = 295,176.96
  5. Step 5: Solve for x
    x = 295,176.96/514.40
  6. Step 6: Final answer
    x = 573.83

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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.