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Finding the Third Proportional to 10,214 and 13,278

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Solution

The third proportional to 10,214 and 13,278 is: 17,261.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,214 : 13,278 = 13,278 : x
  2. Step 2: Convert to fraction form
    10,214/13,278 = 13,278/x
  3. Step 3: Cross multiply
    10,214x = 13,278 × 13,278
  4. Step 4: Simplify right side
    10,214x = 176,305,284
  5. Step 5: Solve for x
    x = 176,305,284/10,214
  6. Step 6: Final answer
    x = 17,261.14

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.