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Finding the Third Proportional to 5,409 and 8,216

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Solution

The third proportional to 5,409 and 8,216 is: 12,479.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,409 : 8,216 = 8,216 : x
  2. Step 2: Convert to fraction form
    5,409/8,216 = 8,216/x
  3. Step 3: Cross multiply
    5,409x = 8,216 × 8,216
  4. Step 4: Simplify right side
    5,409x = 67,502,656
  5. Step 5: Solve for x
    x = 67,502,656/5,409
  6. Step 6: Final answer
    x = 12,479.69

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.