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Finding the Third Proportional to 3,840 and 8,224

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Solution

The third proportional to 3,840 and 8,224 is: 17,613.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,840 : 8,224 = 8,224 : x
  2. Step 2: Convert to fraction form
    3,840/8,224 = 8,224/x
  3. Step 3: Cross multiply
    3,840x = 8,224 × 8,224
  4. Step 4: Simplify right side
    3,840x = 67,634,176
  5. Step 5: Solve for x
    x = 67,634,176/3,840
  6. Step 6: Final answer
    x = 17,613.07

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.