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Finding the Fourth Proportional to 829, 1,243.50 and 316

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Solution

The fourth proportional to 829, 1,243.50 and 316 is: 474

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,243.50 = 316 : x
  2. Step 2: Convert to fraction form
    829/1,243.50 = 316/x
  3. Step 3: Cross multiply
    829x = 1,243.50 × 316
  4. Step 4: Simplify right side
    829x = 392,946
  5. Step 5: Solve for x
    x = 392,946/829
  6. Step 6: Final answer
    x = 474

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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.