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Finding the Third Proportional to 103,409 and 214,498

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Solution

The third proportional to 103,409 and 214,498 is: 444,926.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    103,409 : 214,498 = 214,498 : x
  2. Step 2: Convert to fraction form
    103,409/214,498 = 214,498/x
  3. Step 3: Cross multiply
    103,409x = 214,498 × 214,498
  4. Step 4: Simplify right side
    103,409x = 46,009,392,004
  5. Step 5: Solve for x
    x = 46,009,392,004/103,409
  6. Step 6: Final answer
    x = 444,926.38

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.