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Finding the Third Proportional to 1,782 and 3,609

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Solution

The third proportional to 1,782 and 3,609 is: 7,309.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,782 : 3,609 = 3,609 : x
  2. Step 2: Convert to fraction form
    1,782/3,609 = 3,609/x
  3. Step 3: Cross multiply
    1,782x = 3,609 × 3,609
  4. Step 4: Simplify right side
    1,782x = 13,024,881
  5. Step 5: Solve for x
    x = 13,024,881/1,782
  6. Step 6: Final answer
    x = 7,309.14

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.