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Finding the Third Proportional to 3,540 and 8,410

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Solution

The third proportional to 3,540 and 8,410 is: 19,979.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,540 : 8,410 = 8,410 : x
  2. Step 2: Convert to fraction form
    3,540/8,410 = 8,410/x
  3. Step 3: Cross multiply
    3,540x = 8,410 × 8,410
  4. Step 4: Simplify right side
    3,540x = 70,728,100
  5. Step 5: Solve for x
    x = 70,728,100/3,540
  6. Step 6: Final answer
    x = 19,979.69

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.