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Finding the Third Proportional to 2,024 and 2,296

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Solution

The third proportional to 2,024 and 2,296 is: 2,604.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,024 : 2,296 = 2,296 : x
  2. Step 2: Convert to fraction form
    2,024/2,296 = 2,296/x
  3. Step 3: Cross multiply
    2,024x = 2,296 × 2,296
  4. Step 4: Simplify right side
    2,024x = 5,271,616
  5. Step 5: Solve for x
    x = 5,271,616/2,024
  6. Step 6: Final answer
    x = 2,604.55

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.