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Finding the Third Proportional to 820 and 2,014

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Solution

The third proportional to 820 and 2,014 is: 4,946.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    820 : 2,014 = 2,014 : x
  2. Step 2: Convert to fraction form
    820/2,014 = 2,014/x
  3. Step 3: Cross multiply
    820x = 2,014 × 2,014
  4. Step 4: Simplify right side
    820x = 4,056,196
  5. Step 5: Solve for x
    x = 4,056,196/820
  6. Step 6: Final answer
    x = 4,946.58

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Why These Related Problems?

These problems maintain the same ratio (2.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.