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Finding the Third Proportional to 24,823 and 53,201

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Solution

The third proportional to 24,823 and 53,201 is: 114,021.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    24,823 : 53,201 = 53,201 : x
  2. Step 2: Convert to fraction form
    24,823/53,201 = 53,201/x
  3. Step 3: Cross multiply
    24,823x = 53,201 × 53,201
  4. Step 4: Simplify right side
    24,823x = 2,830,346,401
  5. Step 5: Solve for x
    x = 2,830,346,401/24,823
  6. Step 6: Final answer
    x = 114,021.13

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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.