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Finding the Third Proportional to 1,029 and 1,233

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Solution

The third proportional to 1,029 and 1,233 is: 1,477.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029 : 1,233 = 1,233 : x
  2. Step 2: Convert to fraction form
    1,029/1,233 = 1,233/x
  3. Step 3: Cross multiply
    1,029x = 1,233 × 1,233
  4. Step 4: Simplify right side
    1,029x = 1,520,289
  5. Step 5: Solve for x
    x = 1,520,289/1,029
  6. Step 6: Final answer
    x = 1,477.44

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.