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Finding the Third Proportional to 4,196 and 7,856

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Solution

The third proportional to 4,196 and 7,856 is: 14,708.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,196 : 7,856 = 7,856 : x
  2. Step 2: Convert to fraction form
    4,196/7,856 = 7,856/x
  3. Step 3: Cross multiply
    4,196x = 7,856 × 7,856
  4. Step 4: Simplify right side
    4,196x = 61,716,736
  5. Step 5: Solve for x
    x = 61,716,736/4,196
  6. Step 6: Final answer
    x = 14,708.47

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.