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Finding the Third Proportional to 14,214 and 31,278

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Solution

The third proportional to 14,214 and 31,278 is: 68,827.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,214 : 31,278 = 31,278 : x
  2. Step 2: Convert to fraction form
    14,214/31,278 = 31,278/x
  3. Step 3: Cross multiply
    14,214x = 31,278 × 31,278
  4. Step 4: Simplify right side
    14,214x = 978,313,284
  5. Step 5: Solve for x
    x = 978,313,284/14,214
  6. Step 6: Final answer
    x = 68,827.44

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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.