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Finding the Third Proportional to 7,840 and 18,224

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Solution

The third proportional to 7,840 and 18,224 is: 42,361.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,840 : 18,224 = 18,224 : x
  2. Step 2: Convert to fraction form
    7,840/18,224 = 18,224/x
  3. Step 3: Cross multiply
    7,840x = 18,224 × 18,224
  4. Step 4: Simplify right side
    7,840x = 332,114,176
  5. Step 5: Solve for x
    x = 332,114,176/7,840
  6. Step 6: Final answer
    x = 42,361.50

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.