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Finding the Third Proportional to 82,971 and 121,530

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Solution

The third proportional to 82,971 and 121,530 is: 178,008.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,971 : 121,530 = 121,530 : x
  2. Step 2: Convert to fraction form
    82,971/121,530 = 121,530/x
  3. Step 3: Cross multiply
    82,971x = 121,530 × 121,530
  4. Step 4: Simplify right side
    82,971x = 14,769,540,900
  5. Step 5: Solve for x
    x = 14,769,540,900/82,971
  6. Step 6: Final answer
    x = 178,008.47

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.