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Finding the Third Proportional to 414.56 and 688.22

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Solution

The third proportional to 414.56 and 688.22 is: 1,142.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.56 : 688.22 = 688.22 : x
  2. Step 2: Convert to fraction form
    414.56/688.22 = 688.22/x
  3. Step 3: Cross multiply
    414.56x = 688.22 × 688.22
  4. Step 4: Simplify right side
    414.56x = 473,645.05
  5. Step 5: Solve for x
    x = 473,645.05/414.56
  6. Step 6: Final answer
    x = 1,142.52

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.