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Finding the Fourth Proportional to 686, 946.80 and 410

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Solution

The fourth proportional to 686, 946.80 and 410 is: 565.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 946.80 = 410 : x
  2. Step 2: Convert to fraction form
    686/946.80 = 410/x
  3. Step 3: Cross multiply
    686x = 946.80 × 410
  4. Step 4: Simplify right side
    686x = 388,188
  5. Step 5: Solve for x
    x = 388,188/686
  6. Step 6: Final answer
    x = 565.87

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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.