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Finding the Fourth Proportional to 774.28, 1,160.46 and 409

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Solution

The fourth proportional to 774.28, 1,160.46 and 409 is: 612.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    774.28 : 1,160.46 = 409 : x
  2. Step 2: Convert to fraction form
    774.28/1,160.46 = 409/x
  3. Step 3: Cross multiply
    774.28x = 1,160.46 × 409
  4. Step 4: Simplify right side
    774.28x = 474,628.14
  5. Step 5: Solve for x
    x = 474,628.14/774.28
  6. Step 6: Final answer
    x = 612.99

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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.