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Finding the Third Proportional to 312.94 and 419.95

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Solution

The third proportional to 312.94 and 419.95 is: 563.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    312.94 : 419.95 = 419.95 : x
  2. Step 2: Convert to fraction form
    312.94/419.95 = 419.95/x
  3. Step 3: Cross multiply
    312.94x = 419.95 × 419.95
  4. Step 4: Simplify right side
    312.94x = 176,360.63
  5. Step 5: Solve for x
    x = 176,360.63/312.94
  6. Step 6: Final answer
    x = 563.57

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.