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Finding the Third Proportional to 1,580 and 3,584

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Solution

The third proportional to 1,580 and 3,584 is: 8,129.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,580 : 3,584 = 3,584 : x
  2. Step 2: Convert to fraction form
    1,580/3,584 = 3,584/x
  3. Step 3: Cross multiply
    1,580x = 3,584 × 3,584
  4. Step 4: Simplify right side
    1,580x = 12,845,056
  5. Step 5: Solve for x
    x = 12,845,056/1,580
  6. Step 6: Final answer
    x = 8,129.78

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Why These Related Problems?

These problems maintain the same ratio (2.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.