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Finding the Third Proportional to 38,540 and 83,284

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Solution

The third proportional to 38,540 and 83,284 is: 179,974.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,540 : 83,284 = 83,284 : x
  2. Step 2: Convert to fraction form
    38,540/83,284 = 83,284/x
  3. Step 3: Cross multiply
    38,540x = 83,284 × 83,284
  4. Step 4: Simplify right side
    38,540x = 6,936,224,656
  5. Step 5: Solve for x
    x = 6,936,224,656/38,540
  6. Step 6: Final answer
    x = 179,974.69

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.