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Finding the Third Proportional to 821 and 1,253

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Solution

The third proportional to 821 and 1,253 is: 1,912.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    821 : 1,253 = 1,253 : x
  2. Step 2: Convert to fraction form
    821/1,253 = 1,253/x
  3. Step 3: Cross multiply
    821x = 1,253 × 1,253
  4. Step 4: Simplify right side
    821x = 1,570,009
  5. Step 5: Solve for x
    x = 1,570,009/821
  6. Step 6: Final answer
    x = 1,912.31

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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.