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Finding the Third Proportional to 2,084 and 4,490

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Solution

The third proportional to 2,084 and 4,490 is: 9,673.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,084 : 4,490 = 4,490 : x
  2. Step 2: Convert to fraction form
    2,084/4,490 = 4,490/x
  3. Step 3: Cross multiply
    2,084x = 4,490 × 4,490
  4. Step 4: Simplify right side
    2,084x = 20,160,100
  5. Step 5: Solve for x
    x = 20,160,100/2,084
  6. Step 6: Final answer
    x = 9,673.75

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.