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Finding the Third Proportional to 97,776 and 208,224

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Solution

The third proportional to 97,776 and 208,224 is: 443,434.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,776 : 208,224 = 208,224 : x
  2. Step 2: Convert to fraction form
    97,776/208,224 = 208,224/x
  3. Step 3: Cross multiply
    97,776x = 208,224 × 208,224
  4. Step 4: Simplify right side
    97,776x = 43,357,234,176
  5. Step 5: Solve for x
    x = 43,357,234,176/97,776
  6. Step 6: Final answer
    x = 443,434.32

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.