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Finding the Third Proportional to 823.50 and 1,232.16

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Solution

The third proportional to 823.50 and 1,232.16 is: 1,843.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.50 : 1,232.16 = 1,232.16 : x
  2. Step 2: Convert to fraction form
    823.50/1,232.16 = 1,232.16/x
  3. Step 3: Cross multiply
    823.50x = 1,232.16 × 1,232.16
  4. Step 4: Simplify right side
    823.50x = 1,518,209.02
  5. Step 5: Solve for x
    x = 1,518,209.02/823.50
  6. Step 6: Final answer
    x = 1,843.61

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.