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Finding the Third Proportional to 785 and 1,205

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Solution

The third proportional to 785 and 1,205 is: 1,849.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    785 : 1,205 = 1,205 : x
  2. Step 2: Convert to fraction form
    785/1,205 = 1,205/x
  3. Step 3: Cross multiply
    785x = 1,205 × 1,205
  4. Step 4: Simplify right side
    785x = 1,452,025
  5. Step 5: Solve for x
    x = 1,452,025/785
  6. Step 6: Final answer
    x = 1,849.71

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.