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Finding the Third Proportional to 38,102 and 83,566

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Solution

The third proportional to 38,102 and 83,566 is: 183,278.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,102 : 83,566 = 83,566 : x
  2. Step 2: Convert to fraction form
    38,102/83,566 = 83,566/x
  3. Step 3: Cross multiply
    38,102x = 83,566 × 83,566
  4. Step 4: Simplify right side
    38,102x = 6,983,276,356
  5. Step 5: Solve for x
    x = 6,983,276,356/38,102
  6. Step 6: Final answer
    x = 183,278.47

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.