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Finding the Third Proportional to 456.75 and 685.13

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Solution

The third proportional to 456.75 and 685.13 is: 1,027.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.75 : 685.13 = 685.13 : x
  2. Step 2: Convert to fraction form
    456.75/685.13 = 685.13/x
  3. Step 3: Cross multiply
    456.75x = 685.13 × 685.13
  4. Step 4: Simplify right side
    456.75x = 469,396.27
  5. Step 5: Solve for x
    x = 469,396.27/456.75
  6. Step 6: Final answer
    x = 1,027.69

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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.