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Finding the Third Proportional to 1,731 and 1,785

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Solution

The third proportional to 1,731 and 1,785 is: 1,840.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,731 : 1,785 = 1,785 : x
  2. Step 2: Convert to fraction form
    1,731/1,785 = 1,785/x
  3. Step 3: Cross multiply
    1,731x = 1,785 × 1,785
  4. Step 4: Simplify right side
    1,731x = 3,186,225
  5. Step 5: Solve for x
    x = 3,186,225/1,731
  6. Step 6: Final answer
    x = 1,840.68

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Why These Related Problems?

These problems maintain the same ratio (1.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.