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Finding the Third Proportional to 870 and 2,049

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Solution

The third proportional to 870 and 2,049 is: 4,825.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    870 : 2,049 = 2,049 : x
  2. Step 2: Convert to fraction form
    870/2,049 = 2,049/x
  3. Step 3: Cross multiply
    870x = 2,049 × 2,049
  4. Step 4: Simplify right side
    870x = 4,198,401
  5. Step 5: Solve for x
    x = 4,198,401/870
  6. Step 6: Final answer
    x = 4,825.75

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.