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Finding the Third Proportional to 2,830 and 6,514

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Solution

The third proportional to 2,830 and 6,514 is: 14,993.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,830 : 6,514 = 6,514 : x
  2. Step 2: Convert to fraction form
    2,830/6,514 = 6,514/x
  3. Step 3: Cross multiply
    2,830x = 6,514 × 6,514
  4. Step 4: Simplify right side
    2,830x = 42,432,196
  5. Step 5: Solve for x
    x = 42,432,196/2,830
  6. Step 6: Final answer
    x = 14,993.71

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.