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Finding the Third Proportional to 2,046 and 3,980

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Solution

The third proportional to 2,046 and 3,980 is: 7,742.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,046 : 3,980 = 3,980 : x
  2. Step 2: Convert to fraction form
    2,046/3,980 = 3,980/x
  3. Step 3: Cross multiply
    2,046x = 3,980 × 3,980
  4. Step 4: Simplify right side
    2,046x = 15,840,400
  5. Step 5: Solve for x
    x = 15,840,400/2,046
  6. Step 6: Final answer
    x = 7,742.13

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.