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Finding the Third Proportional to 312.13 and 456.91

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Solution

The third proportional to 312.13 and 456.91 is: 668.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    312.13 : 456.91 = 456.91 : x
  2. Step 2: Convert to fraction form
    312.13/456.91 = 456.91/x
  3. Step 3: Cross multiply
    312.13x = 456.91 × 456.91
  4. Step 4: Simplify right side
    312.13x = 208,763.32
  5. Step 5: Solve for x
    x = 208,763.32/312.13
  6. Step 6: Final answer
    x = 668.85

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.