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Finding the Third Proportional to 5,830 and 10,310

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Solution

The third proportional to 5,830 and 10,310 is: 18,232.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,830 : 10,310 = 10,310 : x
  2. Step 2: Convert to fraction form
    5,830/10,310 = 10,310/x
  3. Step 3: Cross multiply
    5,830x = 10,310 × 10,310
  4. Step 4: Simplify right side
    5,830x = 106,296,100
  5. Step 5: Solve for x
    x = 106,296,100/5,830
  6. Step 6: Final answer
    x = 18,232.61

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.