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Finding the Third Proportional to 53,414 and 83,036

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Solution

The third proportional to 53,414 and 83,036 is: 129,085.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,414 : 83,036 = 83,036 : x
  2. Step 2: Convert to fraction form
    53,414/83,036 = 83,036/x
  3. Step 3: Cross multiply
    53,414x = 83,036 × 83,036
  4. Step 4: Simplify right side
    53,414x = 6,894,977,296
  5. Step 5: Solve for x
    x = 6,894,977,296/53,414
  6. Step 6: Final answer
    x = 129,085.58

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.