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Finding the Fourth Proportional to 1,310, 1,965 and 398

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Solution

The fourth proportional to 1,310, 1,965 and 398 is: 597

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,310 : 1,965 = 398 : x
  2. Step 2: Convert to fraction form
    1,310/1,965 = 398/x
  3. Step 3: Cross multiply
    1,310x = 1,965 × 398
  4. Step 4: Simplify right side
    1,310x = 782,070
  5. Step 5: Solve for x
    x = 782,070/1,310
  6. Step 6: Final answer
    x = 597

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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.