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Finding the Third Proportional to 11,416 and 23,984

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Solution

The third proportional to 11,416 and 23,984 is: 50,388.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    11,416 : 23,984 = 23,984 : x
  2. Step 2: Convert to fraction form
    11,416/23,984 = 23,984/x
  3. Step 3: Cross multiply
    11,416x = 23,984 × 23,984
  4. Step 4: Simplify right side
    11,416x = 575,232,256
  5. Step 5: Solve for x
    x = 575,232,256/11,416
  6. Step 6: Final answer
    x = 50,388.25

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.