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Finding the Third Proportional to 5,202 and 8,514

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Solution

The third proportional to 5,202 and 8,514 is: 13,934.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,202 : 8,514 = 8,514 : x
  2. Step 2: Convert to fraction form
    5,202/8,514 = 8,514/x
  3. Step 3: Cross multiply
    5,202x = 8,514 × 8,514
  4. Step 4: Simplify right side
    5,202x = 72,488,196
  5. Step 5: Solve for x
    x = 72,488,196/5,202
  6. Step 6: Final answer
    x = 13,934.68

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.