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Finding the Third Proportional to 1,832 and 4,216

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Solution

The third proportional to 1,832 and 4,216 is: 9,702.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,832 : 4,216 = 4,216 : x
  2. Step 2: Convert to fraction form
    1,832/4,216 = 4,216/x
  3. Step 3: Cross multiply
    1,832x = 4,216 × 4,216
  4. Step 4: Simplify right side
    1,832x = 17,774,656
  5. Step 5: Solve for x
    x = 17,774,656/1,832
  6. Step 6: Final answer
    x = 9,702.32

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.