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Finding the Third Proportional to 82,576 and 178,400

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Solution

The third proportional to 82,576 and 178,400 is: 385,421.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,576 : 178,400 = 178,400 : x
  2. Step 2: Convert to fraction form
    82,576/178,400 = 178,400/x
  3. Step 3: Cross multiply
    82,576x = 178,400 × 178,400
  4. Step 4: Simplify right side
    82,576x = 31,826,560,000
  5. Step 5: Solve for x
    x = 31,826,560,000/82,576
  6. Step 6: Final answer
    x = 385,421.43

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.