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Finding the Third Proportional to 312.29 and 457.05

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Solution

The third proportional to 312.29 and 457.05 is: 668.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    312.29 : 457.05 = 457.05 : x
  2. Step 2: Convert to fraction form
    312.29/457.05 = 457.05/x
  3. Step 3: Cross multiply
    312.29x = 457.05 × 457.05
  4. Step 4: Simplify right side
    312.29x = 208,893.63
  5. Step 5: Solve for x
    x = 208,893.63/312.29
  6. Step 6: Final answer
    x = 668.90

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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.