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Finding the Third Proportional to 12,416 and 27,284

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Solution

The third proportional to 12,416 and 27,284 is: 59,956.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,416 : 27,284 = 27,284 : x
  2. Step 2: Convert to fraction form
    12,416/27,284 = 27,284/x
  3. Step 3: Cross multiply
    12,416x = 27,284 × 27,284
  4. Step 4: Simplify right side
    12,416x = 744,416,656
  5. Step 5: Solve for x
    x = 744,416,656/12,416
  6. Step 6: Final answer
    x = 59,956.24

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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.