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Finding the Third Proportional to 4,175 and 7,823

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Solution

The third proportional to 4,175 and 7,823 is: 14,658.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,175 : 7,823 = 7,823 : x
  2. Step 2: Convert to fraction form
    4,175/7,823 = 7,823/x
  3. Step 3: Cross multiply
    4,175x = 7,823 × 7,823
  4. Step 4: Simplify right side
    4,175x = 61,199,329
  5. Step 5: Solve for x
    x = 61,199,329/4,175
  6. Step 6: Final answer
    x = 14,658.52

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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.