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Finding the Third Proportional to 201,802 and 416,729

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Solution

The third proportional to 201,802 and 416,729 is: 860,561.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    201,802 : 416,729 = 416,729 : x
  2. Step 2: Convert to fraction form
    201,802/416,729 = 416,729/x
  3. Step 3: Cross multiply
    201,802x = 416,729 × 416,729
  4. Step 4: Simplify right side
    201,802x = 173,663,059,441
  5. Step 5: Solve for x
    x = 173,663,059,441/201,802
  6. Step 6: Final answer
    x = 860,561.64

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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.