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Finding the Third Proportional to 77,357 and 164,070

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Solution

The third proportional to 77,357 and 164,070 is: 347,983.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,357 : 164,070 = 164,070 : x
  2. Step 2: Convert to fraction form
    77,357/164,070 = 164,070/x
  3. Step 3: Cross multiply
    77,357x = 164,070 × 164,070
  4. Step 4: Simplify right side
    77,357x = 26,918,964,900
  5. Step 5: Solve for x
    x = 26,918,964,900/77,357
  6. Step 6: Final answer
    x = 347,983.57

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.