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Finding the Third Proportional to 121,684 and 178,322

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Solution

The third proportional to 121,684 and 178,322 is: 261,322.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    121,684 : 178,322 = 178,322 : x
  2. Step 2: Convert to fraction form
    121,684/178,322 = 178,322/x
  3. Step 3: Cross multiply
    121,684x = 178,322 × 178,322
  4. Step 4: Simplify right side
    121,684x = 31,798,735,684
  5. Step 5: Solve for x
    x = 31,798,735,684/121,684
  6. Step 6: Final answer
    x = 261,322.24

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.