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Finding the Third Proportional to 456.69 and 682.06

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Solution

The third proportional to 456.69 and 682.06 is: 1,018.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.69 : 682.06 = 682.06 : x
  2. Step 2: Convert to fraction form
    456.69/682.06 = 682.06/x
  3. Step 3: Cross multiply
    456.69x = 682.06 × 682.06
  4. Step 4: Simplify right side
    456.69x = 465,209.25
  5. Step 5: Solve for x
    x = 465,209.25/456.69
  6. Step 6: Final answer
    x = 1,018.66

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.