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Finding the Third Proportional to 1,026 and 2,194

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Solution

The third proportional to 1,026 and 2,194 is: 4,691.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,026 : 2,194 = 2,194 : x
  2. Step 2: Convert to fraction form
    1,026/2,194 = 2,194/x
  3. Step 3: Cross multiply
    1,026x = 2,194 × 2,194
  4. Step 4: Simplify right side
    1,026x = 4,813,636
  5. Step 5: Solve for x
    x = 4,813,636/1,026
  6. Step 6: Final answer
    x = 4,691.65

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.