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Finding the Third Proportional to 2,194 and 2,382

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Solution

The third proportional to 2,194 and 2,382 is: 2,586.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,194 : 2,382 = 2,382 : x
  2. Step 2: Convert to fraction form
    2,194/2,382 = 2,382/x
  3. Step 3: Cross multiply
    2,194x = 2,382 × 2,382
  4. Step 4: Simplify right side
    2,194x = 5,673,924
  5. Step 5: Solve for x
    x = 5,673,924/2,194
  6. Step 6: Final answer
    x = 2,586.11

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.