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Finding the Third Proportional to 769.50 and 1,684.13

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Solution

The third proportional to 769.50 and 1,684.13 is: 3,685.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    769.50 : 1,684.13 = 1,684.13 : x
  2. Step 2: Convert to fraction form
    769.50/1,684.13 = 1,684.13/x
  3. Step 3: Cross multiply
    769.50x = 1,684.13 × 1,684.13
  4. Step 4: Simplify right side
    769.50x = 2,836,277.02
  5. Step 5: Solve for x
    x = 2,836,277.02/769.50
  6. Step 6: Final answer
    x = 3,685.87

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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.