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Finding the Third Proportional to 2,097 and 4,221

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Solution

The third proportional to 2,097 and 4,221 is: 8,496.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,097 : 4,221 = 4,221 : x
  2. Step 2: Convert to fraction form
    2,097/4,221 = 4,221/x
  3. Step 3: Cross multiply
    2,097x = 4,221 × 4,221
  4. Step 4: Simplify right side
    2,097x = 17,816,841
  5. Step 5: Solve for x
    x = 17,816,841/2,097
  6. Step 6: Final answer
    x = 8,496.35

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Why These Related Problems?

These problems maintain the same ratio (2.01) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.