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Finding the Third Proportional to 1,580 and 2,114

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Solution

The third proportional to 1,580 and 2,114 is: 2,828.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,580 : 2,114 = 2,114 : x
  2. Step 2: Convert to fraction form
    1,580/2,114 = 2,114/x
  3. Step 3: Cross multiply
    1,580x = 2,114 × 2,114
  4. Step 4: Simplify right side
    1,580x = 4,468,996
  5. Step 5: Solve for x
    x = 4,468,996/1,580
  6. Step 6: Final answer
    x = 2,828.48

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.