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Finding the Third Proportional to 2,209 and 4,105

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Solution

The third proportional to 2,209 and 4,105 is: 7,628.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,209 : 4,105 = 4,105 : x
  2. Step 2: Convert to fraction form
    2,209/4,105 = 4,105/x
  3. Step 3: Cross multiply
    2,209x = 4,105 × 4,105
  4. Step 4: Simplify right side
    2,209x = 16,851,025
  5. Step 5: Solve for x
    x = 16,851,025/2,209
  6. Step 6: Final answer
    x = 7,628.35

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.