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Finding the Third Proportional to 53,464 and 82,019

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Solution

The third proportional to 53,464 and 82,019 is: 125,825.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,464 : 82,019 = 82,019 : x
  2. Step 2: Convert to fraction form
    53,464/82,019 = 82,019/x
  3. Step 3: Cross multiply
    53,464x = 82,019 × 82,019
  4. Step 4: Simplify right side
    53,464x = 6,727,116,361
  5. Step 5: Solve for x
    x = 6,727,116,361/53,464
  6. Step 6: Final answer
    x = 125,825.16

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.