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Finding the Third Proportional to 57,971 and 82,677

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Solution

The third proportional to 57,971 and 82,677 is: 117,912.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    57,971 : 82,677 = 82,677 : x
  2. Step 2: Convert to fraction form
    57,971/82,677 = 82,677/x
  3. Step 3: Cross multiply
    57,971x = 82,677 × 82,677
  4. Step 4: Simplify right side
    57,971x = 6,835,486,329
  5. Step 5: Solve for x
    x = 6,835,486,329/57,971
  6. Step 6: Final answer
    x = 117,912.17

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.