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Finding the Third Proportional to 37,779 and 82,823

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Solution

The third proportional to 37,779 and 82,823 is: 181,573.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,779 : 82,823 = 82,823 : x
  2. Step 2: Convert to fraction form
    37,779/82,823 = 82,823/x
  3. Step 3: Cross multiply
    37,779x = 82,823 × 82,823
  4. Step 4: Simplify right side
    37,779x = 6,859,649,329
  5. Step 5: Solve for x
    x = 6,859,649,329/37,779
  6. Step 6: Final answer
    x = 181,573.08

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.