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Finding the Fourth Proportional to 522.14, 784.10 and 463.70

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Solution

The fourth proportional to 522.14, 784.10 and 463.70 is: 696.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    522.14 : 784.10 = 463.70 : x
  2. Step 2: Convert to fraction form
    522.14/784.10 = 463.70/x
  3. Step 3: Cross multiply
    522.14x = 784.10 × 463.70
  4. Step 4: Simplify right side
    522.14x = 363,590.29
  5. Step 5: Solve for x
    x = 363,590.29/522.14
  6. Step 6: Final answer
    x = 696.35

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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.