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Finding the Third Proportional to 3,514 and 6,830

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Solution

The third proportional to 3,514 and 6,830 is: 13,275.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,514 : 6,830 = 6,830 : x
  2. Step 2: Convert to fraction form
    3,514/6,830 = 6,830/x
  3. Step 3: Cross multiply
    3,514x = 6,830 × 6,830
  4. Step 4: Simplify right side
    3,514x = 46,648,900
  5. Step 5: Solve for x
    x = 46,648,900/3,514
  6. Step 6: Final answer
    x = 13,275.16

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Why These Related Problems?

These problems maintain the same ratio (1.94) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.