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Finding the Third Proportional to 823 and 1,223

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Solution

The third proportional to 823 and 1,223 is: 1,817.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    823 : 1,223 = 1,223 : x
  2. Step 2: Convert to fraction form
    823/1,223 = 1,223/x
  3. Step 3: Cross multiply
    823x = 1,223 × 1,223
  4. Step 4: Simplify right side
    823x = 1,495,729
  5. Step 5: Solve for x
    x = 1,495,729/823
  6. Step 6: Final answer
    x = 1,817.41

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.