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Finding the Third Proportional to 2,590 and 5,420

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Solution

The third proportional to 2,590 and 5,420 is: 11,342.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,590 : 5,420 = 5,420 : x
  2. Step 2: Convert to fraction form
    2,590/5,420 = 5,420/x
  3. Step 3: Cross multiply
    2,590x = 5,420 × 5,420
  4. Step 4: Simplify right side
    2,590x = 29,376,400
  5. Step 5: Solve for x
    x = 29,376,400/2,590
  6. Step 6: Final answer
    x = 11,342.24

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.