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Finding the Third Proportional to 823.50 and 1,206

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Solution

The third proportional to 823.50 and 1,206 is: 1,766.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.50 : 1,206 = 1,206 : x
  2. Step 2: Convert to fraction form
    823.50/1,206 = 1,206/x
  3. Step 3: Cross multiply
    823.50x = 1,206 × 1,206
  4. Step 4: Simplify right side
    823.50x = 1,454,436
  5. Step 5: Solve for x
    x = 1,454,436/823.50
  6. Step 6: Final answer
    x = 1,766.16

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.