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Finding the Third Proportional to 82,971 and 128,133

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Solution

The third proportional to 82,971 and 128,133 is: 197,877.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,971 : 128,133 = 128,133 : x
  2. Step 2: Convert to fraction form
    82,971/128,133 = 128,133/x
  3. Step 3: Cross multiply
    82,971x = 128,133 × 128,133
  4. Step 4: Simplify right side
    82,971x = 16,418,065,689
  5. Step 5: Solve for x
    x = 16,418,065,689/82,971
  6. Step 6: Final answer
    x = 197,877.16

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.