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Finding the Third Proportional to 82,031 and 128,514

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Solution

The third proportional to 82,031 and 128,514 is: 201,336.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,031 : 128,514 = 128,514 : x
  2. Step 2: Convert to fraction form
    82,031/128,514 = 128,514/x
  3. Step 3: Cross multiply
    82,031x = 128,514 × 128,514
  4. Step 4: Simplify right side
    82,031x = 16,515,848,196
  5. Step 5: Solve for x
    x = 16,515,848,196/82,031
  6. Step 6: Final answer
    x = 201,336.67

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.