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Finding the Third Proportional to 97,776 and 214,232

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Solution

The third proportional to 97,776 and 214,232 is: 469,392.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,776 : 214,232 = 214,232 : x
  2. Step 2: Convert to fraction form
    97,776/214,232 = 214,232/x
  3. Step 3: Cross multiply
    97,776x = 214,232 × 214,232
  4. Step 4: Simplify right side
    97,776x = 45,895,349,824
  5. Step 5: Solve for x
    x = 45,895,349,824/97,776
  6. Step 6: Final answer
    x = 469,392.79

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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.