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Finding the Third Proportional to 24,214 and 53,221

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Solution

The third proportional to 24,214 and 53,221 is: 116,976.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    24,214 : 53,221 = 53,221 : x
  2. Step 2: Convert to fraction form
    24,214/53,221 = 53,221/x
  3. Step 3: Cross multiply
    24,214x = 53,221 × 53,221
  4. Step 4: Simplify right side
    24,214x = 2,832,474,841
  5. Step 5: Solve for x
    x = 2,832,474,841/24,214
  6. Step 6: Final answer
    x = 116,976.74

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.