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Finding the Third Proportional to 2,042 and 2,411

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Solution

The third proportional to 2,042 and 2,411 is: 2,846.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,042 : 2,411 = 2,411 : x
  2. Step 2: Convert to fraction form
    2,042/2,411 = 2,411/x
  3. Step 3: Cross multiply
    2,042x = 2,411 × 2,411
  4. Step 4: Simplify right side
    2,042x = 5,812,921
  5. Step 5: Solve for x
    x = 5,812,921/2,042
  6. Step 6: Final answer
    x = 2,846.68

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.