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Finding the Third Proportional to 538.84 and 823.61

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Solution

The third proportional to 538.84 and 823.61 is: 1,258.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    538.84 : 823.61 = 823.61 : x
  2. Step 2: Convert to fraction form
    538.84/823.61 = 823.61/x
  3. Step 3: Cross multiply
    538.84x = 823.61 × 823.61
  4. Step 4: Simplify right side
    538.84x = 678,325.97
  5. Step 5: Solve for x
    x = 678,325.97/538.84
  6. Step 6: Final answer
    x = 1,258.86

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.