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Finding the Third Proportional to 82,030 and 128,509

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Solution

The third proportional to 82,030 and 128,509 is: 201,323.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,030 : 128,509 = 128,509 : x
  2. Step 2: Convert to fraction form
    82,030/128,509 = 128,509/x
  3. Step 3: Cross multiply
    82,030x = 128,509 × 128,509
  4. Step 4: Simplify right side
    82,030x = 16,514,563,081
  5. Step 5: Solve for x
    x = 16,514,563,081/82,030
  6. Step 6: Final answer
    x = 201,323.46

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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.