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Finding the Third Proportional to 456.56 and 684.84

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Solution

The third proportional to 456.56 and 684.84 is: 1,027.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.56 : 684.84 = 684.84 : x
  2. Step 2: Convert to fraction form
    456.56/684.84 = 684.84/x
  3. Step 3: Cross multiply
    456.56x = 684.84 × 684.84
  4. Step 4: Simplify right side
    456.56x = 469,010.96
  5. Step 5: Solve for x
    x = 469,010.96/456.56
  6. Step 6: Final answer
    x = 1,027.27

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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.