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Finding the Third Proportional to 53,802 and 82,971

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Solution

The third proportional to 53,802 and 82,971 is: 127,954.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,802 : 82,971 = 82,971 : x
  2. Step 2: Convert to fraction form
    53,802/82,971 = 82,971/x
  3. Step 3: Cross multiply
    53,802x = 82,971 × 82,971
  4. Step 4: Simplify right side
    53,802x = 6,884,186,841
  5. Step 5: Solve for x
    x = 6,884,186,841/53,802
  6. Step 6: Final answer
    x = 127,954.11

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.