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Finding the Third Proportional to 785 and 1,666

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Solution

The third proportional to 785 and 1,666 is: 3,535.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    785 : 1,666 = 1,666 : x
  2. Step 2: Convert to fraction form
    785/1,666 = 1,666/x
  3. Step 3: Cross multiply
    785x = 1,666 × 1,666
  4. Step 4: Simplify right side
    785x = 2,775,556
  5. Step 5: Solve for x
    x = 2,775,556/785
  6. Step 6: Final answer
    x = 3,535.74

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.