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Finding the Third Proportional to 2,302 and 3,407

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Solution

The third proportional to 2,302 and 3,407 is: 5,042.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,302 : 3,407 = 3,407 : x
  2. Step 2: Convert to fraction form
    2,302/3,407 = 3,407/x
  3. Step 3: Cross multiply
    2,302x = 3,407 × 3,407
  4. Step 4: Simplify right side
    2,302x = 11,607,649
  5. Step 5: Solve for x
    x = 11,607,649/2,302
  6. Step 6: Final answer
    x = 5,042.42

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.