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Finding the Third Proportional to 12,416 and 19,984

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Solution

The third proportional to 12,416 and 19,984 is: 32,164.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,416 : 19,984 = 19,984 : x
  2. Step 2: Convert to fraction form
    12,416/19,984 = 19,984/x
  3. Step 3: Cross multiply
    12,416x = 19,984 × 19,984
  4. Step 4: Simplify right side
    12,416x = 399,360,256
  5. Step 5: Solve for x
    x = 399,360,256/12,416
  6. Step 6: Final answer
    x = 32,164.97

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.