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Finding the Third Proportional to 2,024 and 3,840

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Solution

The third proportional to 2,024 and 3,840 is: 7,285.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,024 : 3,840 = 3,840 : x
  2. Step 2: Convert to fraction form
    2,024/3,840 = 3,840/x
  3. Step 3: Cross multiply
    2,024x = 3,840 × 3,840
  4. Step 4: Simplify right side
    2,024x = 14,745,600
  5. Step 5: Solve for x
    x = 14,745,600/2,024
  6. Step 6: Final answer
    x = 7,285.38

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Why These Related Problems?

These problems maintain the same ratio (1.90) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.