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Finding the Third Proportional to 205,106 and 310,489

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Solution

The third proportional to 205,106 and 310,489 is: 470,017.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,106 : 310,489 = 310,489 : x
  2. Step 2: Convert to fraction form
    205,106/310,489 = 310,489/x
  3. Step 3: Cross multiply
    205,106x = 310,489 × 310,489
  4. Step 4: Simplify right side
    205,106x = 96,403,419,121
  5. Step 5: Solve for x
    x = 96,403,419,121/205,106
  6. Step 6: Final answer
    x = 470,017.55

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.