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Finding the Third Proportional to 982 and 1,578

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Solution

The third proportional to 982 and 1,578 is: 2,535.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    982 : 1,578 = 1,578 : x
  2. Step 2: Convert to fraction form
    982/1,578 = 1,578/x
  3. Step 3: Cross multiply
    982x = 1,578 × 1,578
  4. Step 4: Simplify right side
    982x = 2,490,084
  5. Step 5: Solve for x
    x = 2,490,084/982
  6. Step 6: Final answer
    x = 2,535.73

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.