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Finding the Third Proportional to 823.50 and 2,106

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Solution

The third proportional to 823.50 and 2,106 is: 5,385.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.50 : 2,106 = 2,106 : x
  2. Step 2: Convert to fraction form
    823.50/2,106 = 2,106/x
  3. Step 3: Cross multiply
    823.50x = 2,106 × 2,106
  4. Step 4: Simplify right side
    823.50x = 4,435,236
  5. Step 5: Solve for x
    x = 4,435,236/823.50
  6. Step 6: Final answer
    x = 5,385.84

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Why These Related Problems?

These problems maintain the same ratio (2.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.