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Finding the Third Proportional to 37,719 and 82,971

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Solution

The third proportional to 37,719 and 82,971 is: 182,512.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,719 : 82,971 = 82,971 : x
  2. Step 2: Convert to fraction form
    37,719/82,971 = 82,971/x
  3. Step 3: Cross multiply
    37,719x = 82,971 × 82,971
  4. Step 4: Simplify right side
    37,719x = 6,884,186,841
  5. Step 5: Solve for x
    x = 6,884,186,841/37,719
  6. Step 6: Final answer
    x = 182,512.44

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.