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Finding the Third Proportional to 1,578 and 2,411

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Solution

The third proportional to 1,578 and 2,411 is: 3,683.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,578 : 2,411 = 2,411 : x
  2. Step 2: Convert to fraction form
    1,578/2,411 = 2,411/x
  3. Step 3: Cross multiply
    1,578x = 2,411 × 2,411
  4. Step 4: Simplify right side
    1,578x = 5,812,921
  5. Step 5: Solve for x
    x = 5,812,921/1,578
  6. Step 6: Final answer
    x = 3,683.73

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.