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Finding the Fourth Proportional to 1,606, 2,409 and 580

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Solution

The fourth proportional to 1,606, 2,409 and 580 is: 870

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,606 : 2,409 = 580 : x
  2. Step 2: Convert to fraction form
    1,606/2,409 = 580/x
  3. Step 3: Cross multiply
    1,606x = 2,409 × 580
  4. Step 4: Simplify right side
    1,606x = 1,397,220
  5. Step 5: Solve for x
    x = 1,397,220/1,606
  6. Step 6: Final answer
    x = 870

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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.