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Finding the Third Proportional to 2,590 and 5,702

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Solution

The third proportional to 2,590 and 5,702 is: 12,553.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,590 : 5,702 = 5,702 : x
  2. Step 2: Convert to fraction form
    2,590/5,702 = 5,702/x
  3. Step 3: Cross multiply
    2,590x = 5,702 × 5,702
  4. Step 4: Simplify right side
    2,590x = 32,512,804
  5. Step 5: Solve for x
    x = 32,512,804/2,590
  6. Step 6: Final answer
    x = 12,553.21

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.