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Finding the Third Proportional to 126,416 and 270,824

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Solution

The third proportional to 126,416 and 270,824 is: 580,192.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    126,416 : 270,824 = 270,824 : x
  2. Step 2: Convert to fraction form
    126,416/270,824 = 270,824/x
  3. Step 3: Cross multiply
    126,416x = 270,824 × 270,824
  4. Step 4: Simplify right side
    126,416x = 73,345,638,976
  5. Step 5: Solve for x
    x = 73,345,638,976/126,416
  6. Step 6: Final answer
    x = 580,192.69

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.