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Finding the Fourth Proportional to 1,406, 2,109 and 380

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Solution

The fourth proportional to 1,406, 2,109 and 380 is: 570

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406 : 2,109 = 380 : x
  2. Step 2: Convert to fraction form
    1,406/2,109 = 380/x
  3. Step 3: Cross multiply
    1,406x = 2,109 × 380
  4. Step 4: Simplify right side
    1,406x = 801,420
  5. Step 5: Solve for x
    x = 801,420/1,406
  6. Step 6: Final answer
    x = 570

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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.