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Finding the Third Proportional to 205,874 and 299,429

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Solution

The third proportional to 205,874 and 299,429 is: 435,498.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,874 : 299,429 = 299,429 : x
  2. Step 2: Convert to fraction form
    205,874/299,429 = 299,429/x
  3. Step 3: Cross multiply
    205,874x = 299,429 × 299,429
  4. Step 4: Simplify right side
    205,874x = 89,657,726,041
  5. Step 5: Solve for x
    x = 89,657,726,041/205,874
  6. Step 6: Final answer
    x = 435,498.05

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.