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Finding the Third Proportional to 523 and 1,127

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Solution

The third proportional to 523 and 1,127 is: 2,428.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 1,127 = 1,127 : x
  2. Step 2: Convert to fraction form
    523/1,127 = 1,127/x
  3. Step 3: Cross multiply
    523x = 1,127 × 1,127
  4. Step 4: Simplify right side
    523x = 1,270,129
  5. Step 5: Solve for x
    x = 1,270,129/523
  6. Step 6: Final answer
    x = 2,428.54

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.