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Finding the Third Proportional to 4,266 and 6,416

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Solution

The third proportional to 4,266 and 6,416 is: 9,649.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,266 : 6,416 = 6,416 : x
  2. Step 2: Convert to fraction form
    4,266/6,416 = 6,416/x
  3. Step 3: Cross multiply
    4,266x = 6,416 × 6,416
  4. Step 4: Simplify right side
    4,266x = 41,165,056
  5. Step 5: Solve for x
    x = 41,165,056/4,266
  6. Step 6: Final answer
    x = 9,649.57

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.