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Finding the Third Proportional to 592 and 1,580

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Solution

The third proportional to 592 and 1,580 is: 4,216.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    592 : 1,580 = 1,580 : x
  2. Step 2: Convert to fraction form
    592/1,580 = 1,580/x
  3. Step 3: Cross multiply
    592x = 1,580 × 1,580
  4. Step 4: Simplify right side
    592x = 2,496,400
  5. Step 5: Solve for x
    x = 2,496,400/592
  6. Step 6: Final answer
    x = 4,216.89

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Why These Related Problems?

These problems maintain the same ratio (2.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.