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Finding the Third Proportional to 82,120 and 177,056

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Solution

The third proportional to 82,120 and 177,056 is: 381,744.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,120 : 177,056 = 177,056 : x
  2. Step 2: Convert to fraction form
    82,120/177,056 = 177,056/x
  3. Step 3: Cross multiply
    82,120x = 177,056 × 177,056
  4. Step 4: Simplify right side
    82,120x = 31,348,827,136
  5. Step 5: Solve for x
    x = 31,348,827,136/82,120
  6. Step 6: Final answer
    x = 381,744.12

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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.