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Finding the Third Proportional to 1,690 and 3,649

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Solution

The third proportional to 1,690 and 3,649 is: 7,878.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,690 : 3,649 = 3,649 : x
  2. Step 2: Convert to fraction form
    1,690/3,649 = 3,649/x
  3. Step 3: Cross multiply
    1,690x = 3,649 × 3,649
  4. Step 4: Simplify right side
    1,690x = 13,315,201
  5. Step 5: Solve for x
    x = 13,315,201/1,690
  6. Step 6: Final answer
    x = 7,878.82

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.