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Finding the Third Proportional to 514 and 1,114

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Solution

The third proportional to 514 and 1,114 is: 2,414.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    514 : 1,114 = 1,114 : x
  2. Step 2: Convert to fraction form
    514/1,114 = 1,114/x
  3. Step 3: Cross multiply
    514x = 1,114 × 1,114
  4. Step 4: Simplify right side
    514x = 1,240,996
  5. Step 5: Solve for x
    x = 1,240,996/514
  6. Step 6: Final answer
    x = 2,414.39

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.