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Finding the Third Proportional to 1,829 and 2,045

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Solution

The third proportional to 1,829 and 2,045 is: 2,286.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,829 : 2,045 = 2,045 : x
  2. Step 2: Convert to fraction form
    1,829/2,045 = 2,045/x
  3. Step 3: Cross multiply
    1,829x = 2,045 × 2,045
  4. Step 4: Simplify right side
    1,829x = 4,182,025
  5. Step 5: Solve for x
    x = 4,182,025/1,829
  6. Step 6: Final answer
    x = 2,286.51

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Why These Related Problems?

These problems maintain the same ratio (1.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.